Hoge.php

<?php
class Hoge extends CActiveRecord
{
    public $username; // 追加
    ...

    /**
     * @see CModel::rules()
     */
    public function rules()
    {
        return array(
            array('id, username, fuga, piyo', 'safe', 'on'=>'search'), // user_idをusernameに変更
        );
    }

    /**
     * @see CActiveRecord::relations()
     */
    public function relations()
    {
        return array(
            'user' => array(self::BELONGS_TO, 'User', 'user_id'),
        );
    }

    /**
     * Retrieves a list of models based on the current search/filter conditions.
     * @return CActiveDataProvider the data provider that can return the models based on the search/filter conditions.
     */
    public function search()
    {
        $c = new CDbCriteria();
        $c->with = array('user'); // 追加
        $c->compare('id', $this->id);
        $c->compare('username', $this->username, true); // user_idをusernameに変更
        $c->compare('fuga', $this->fuga, true);
        $c->compare('piyo', $this->piyo, true);
        
        return new CActiveDataProvider(get_class($this), array(
            'criteria' => $c,
            'sort' => array(
                'defaultOrder' => 't.id DESC',
                // usernameがソートできるようにasc, descを設定
                'attributes' => array(
                    'username' => array(
                        'asc' => 'username, t,id',
                        'desc' => 'username DESC, t.id',
                    ),
                    '*', // これは「その他すべて」という意味
                ),
            ),
        ));
    }
}