Forwarding keydown event to a search field

gistfile1.m

- (void)goToProductListWithEvent:(NSEvent *)event
{
    self.selectedViewController = _productListViewController;

    // make the search bar first responder
    NSWindow *window = self.view.window;
    [window makeFirstResponder:_productListViewController.searchField];

    // set the keyDown character into the search field
    _productListViewController.searchField.stringValue = [event characters];

    // need to update filter because this didn't trigger the delegate method
    [_productListViewController updateFilter:_productListViewController.searchField];

    // put the cursor to the right of the character, otherwise it is selected
    NSText *fieldEditor = [window fieldEditor:YES forObject:_productListViewController.searchField];
    
    // do this on next run loop, otherwise it does not work
    dispatch_async(dispatch_get_main_queue(), ^{
        [fieldEditor setSelectedRange:NSMakeRange(1, 0)];
    });
}