Complete working solution for Android action bar tabs with fragments having separate back stack for each tab.

OnItemSelectedListener.java

// Custom interface that enables communication between Fragment and its Activity
public interface OnItemSelectedListener
{
	public void onItemSelected(String item);
}

TabActivity.java

/*
 * This code would not compile as-is. It will require custom Fragment classes, fragment interaction
 * interfaces, animation resources. But it's fully functional in terms of correctly manipulating
 * individual back stacks for each tab, preserving state not only on tab switch but also on device
 * rotation and application switch. To work properly your Fragments should use setRetainInstance(true)
 * or implement their individual state saving via onSaveInstanceState() and state restoring.
 *
 * This code is intentionally as simple as it can be, you can extend it to support custom animations,
 * variable number of tabs, action bar 'up' navigation, etc.
 */
 
import java.util.HashMap;
import java.util.List;
import java.util.Stack;
import java.util.UUID;

import android.os.Bundle;
import android.support.v4.app.Fragment;
import android.support.v4.app.FragmentManager;
import android.support.v4.app.FragmentTransaction;

import com.actionbarsherlock.app.ActionBar;
import com.actionbarsherlock.app.ActionBar.Tab;
import com.actionbarsherlock.app.SherlockFragmentActivity;

// OnItemSelectedListener is a custom interface that enables communication between Fragment and
// its Activity (see bottom of the code for more information)
public class TabActivity extends SherlockFragmentActivity implements ActionBar.TabListener, OnItemSelectedListener
{
	enum TabType
	{
		SEARCH, LIST, FAVORITES
	}

	// Tab back stacks
	private HashMap<TabType, Stack<String>> backStacks;

	@Override
	public void onCreate(Bundle savedInstanceState)
	{
		super.onCreate(savedInstanceState);

		// Initialize ActionBar
		ActionBar bar = getSupportActionBar();
		bar.setNavigationMode(ActionBar.NAVIGATION_MODE_TABS);

		// Set back stacks
		if (savedInstanceState != null)
		{
			// Read back stacks after orientation change
			backStacks = (HashMap<TabType, Stack<String>>) savedInstanceState.getSerializable("stacks");
		}
		else
		{
			// Initialize back stacks on first run
			backStacks = new HashMap<TabType, Stack<String>>();
			backStacks.put(TabType.SEARCH, new Stack<String>());
			backStacks.put(TabType.LIST, new Stack<String>());
			backStacks.put(TabType.FAVORITES, new Stack<String>());
		}
		
		// Create tabs
		bar.addTab(bar.newTab().setTag(TabType.SEARCH).setText("Search").setTabListener(this));
		bar.addTab(bar.newTab().setTag(TabType.LIST).setText("List").setTabListener(this));
		bar.addTab(bar.newTab().setTag(TabType.FAVORITES).setText("Favorites").setTabListener(this));
	}

	@Override
	protected void onResume()
	{
		super.onResume();
		// Select proper stack
		Tab tab = getSupportActionBar().getSelectedTab();
		Stack<String> backStack = backStacks.get(tab.getTag());
		if (! backStack.isEmpty())
		{
			// Restore topmost fragment (e.g. after application switch)
			String tag = backStack.peek();
			Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
			if (fragment.isDetached())
			{
				FragmentTransaction ft = getSupportFragmentManager().beginTransaction();
				ft.attach(fragment);
				ft.commit();
			}
		}
	}

	@Override
	protected void onPause()
	{
		super.onPause();
		// Select proper stack
		Tab tab = getSupportActionBar().getSelectedTab();
		Stack<String> backStack = backStacks.get(tab.getTag());
		if (! backStack.isEmpty())
		{
			// Detach topmost fragment otherwise it will not be correctly displayed
			// after orientation change
			String tag = backStack.peek();
			FragmentTransaction ft = getSupportFragmentManager().beginTransaction();
			Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
			ft.detach(fragment);
			ft.commit();
		}
	}

	@Override
	protected void onRestoreInstanceState(Bundle savedInstanceState)
	{
		super.onRestoreInstanceState(savedInstanceState);
		// Restore selected tab
		int saved = savedInstanceState.getInt("tab", 0);
		if (saved != getSupportActionBar().getSelectedNavigationIndex())
			getSupportActionBar().setSelectedNavigationItem(saved);
	}

	@Override
	protected void onSaveInstanceState(Bundle outState)
	{
		super.onSaveInstanceState(outState);
		// Save selected tab and all back stacks
		outState.putInt("tab", getSupportActionBar().getSelectedNavigationIndex());
		outState.putSerializable("stacks", backStacks);
	}

	@Override
	public void onBackPressed()
	{
		// Select proper stack
		Tab tab = getSupportActionBar().getSelectedTab();
		Stack<String> backStack = backStacks.get(tab.getTag());
		String tag = backStack.pop();
		if (backStack.isEmpty())
		{
			// Let application finish
			super.onBackPressed();
		}
		else
		{
			FragmentTransaction ft = getSupportFragmentManager().beginTransaction();
			Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
			// Animate return to previous fragment
			ft.setCustomAnimations(R.anim.slide_from_right, R.anim.slide_to_left);
			// Remove topmost fragment from back stack and forget it
			ft.remove(fragment);
			showFragment(backStack, ft);
			ft.commit();
		}
	}

	@Override
	public void onTabSelected(Tab tab, FragmentTransaction ft)
	{
		// Select proper stack
		Stack<String> backStack = backStacks.get(tab.getTag());
		if (backStack.isEmpty())
		{
			// If it is empty instantiate and add initial tab fragment
			Fragment fragment;
			switch ((TabType) tab.getTag())
			{
				case SEARCH:
					fragment = Fragment.instantiate(this, SearchFragment.class.getName());
					break;
				case LIST:
					fragment = Fragment.instantiate(this, ListFragment.class.getName());
					break;
				case FAVORITES:
					fragment = Fragment.instantiate(this, FavoritesFragment.class.getName());
					break;
				default:
					throw new java.lang.IllegalArgumentException("Unknown tab");
			}
			addFragment(fragment, backStack, ft);
		}
		else
		{
			// Show topmost fragment
			showFragment(backStack, ft);
		}
	}

	@Override
	public void onTabUnselected(Tab tab, FragmentTransaction ft)
	{
		// Select proper stack
		Stack<String> backStack = backStacks.get(tab.getTag());
		// Get topmost fragment
		String tag = backStack.peek();
		Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
		// Detach it
		ft.detach(fragment);
	}

	@Override
	public void onTabReselected(Tab tab, FragmentTransaction ft)
	{
		// Select proper stack
		Stack<String> backStack = backStacks.get(tab.getTag());

		if (backStack.size() > 1)
			ft.setCustomAnimations(R.anim.slide_from_right, R.anim.slide_to_left);
		// Clean the stack leaving only initial fragment
		while (backStack.size() > 1)
		{
			// Pop topmost fragment
			String tag = backStack.pop();
			Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
			// Remove it
			ft.remove(fragment);
		}
		showFragment(backStack, ft);
	}

	private void addFragment(Fragment fragment)
	{
		// Select proper stack
		Tab tab = getSupportActionBar().getSelectedTab();
		Stack<String> backStack = backStacks.get(tab.getTag());

		FragmentTransaction ft = getSupportFragmentManager().beginTransaction();
		// Animate transfer to new fragment
		ft.setCustomAnimations(R.anim.slide_from_left, R.anim.slide_to_right);
		// Get topmost fragment
		String tag = backStack.peek();
		Fragment top = getSupportFragmentManager().findFragmentByTag(tag);
		ft.detach(top);
		// Add new fragment
		addFragment(fragment, backStack, ft);
		ft.commit();
	}

	private void addFragment(Fragment fragment, Stack<String> backStack, FragmentTransaction ft)
	{
		// Add fragment to back stack with unique tag
		String tag = UUID.randomUUID().toString();
		ft.add(android.R.id.content, fragment, tag);
		backStack.push(tag);
	}

	private void showFragment(Stack<String> backStack, FragmentTransaction ft)
	{
		// Peek topmost fragment from the stack
		String tag = backStack.peek();
		Fragment fragment = getSupportFragmentManager().findFragmentByTag(tag);
		// and attach it
		ft.attach(fragment);		
	}

	// The following code shows how to properly open new fragment. It assumes
	// that parent fragment calls its activity via interface. This approach
	// is described in Android development guidelines.
	@Override
	public void onItemSelected(String item)
	{
		ItemFragment fragment = new ItemFragment();
		Bundle args = new Bundle();
		args.putString("item", item);
		fragment.setArguments(args);
		addFragment(fragment);
	}
}