Add this to your protected/components/Controller.php class to allow mixed cache keys in Yii: $this->beginCache($product)

Controller.php

<?php
/**
 * Controller is the customized base controller class.
 * All controller classes for this application should extend from this base class.
 */
class Controller extends CController
{
  
  // Rest of the Controller class


	/**
	 * Calculates a string ID for any kind of input.
	 *
	 * Used primarily for {@link beginCache()}
	 * @var mixed $id_data Any kind of input data
	 * @return string Hashed string of input data
	 */
	function getHashedID($id_data){
	// Scalar types go as-is
		if(is_scalar($id_data)){
		// Scalar types first
			return (string)$id_data;
		}
	// Arrays are mapped recursively and joined with "/"
		elseif (is_array($id_data)) {
			return join("/", array_map(array($this,'getHashedID'), $id_data));
		}
	// CModels are mapped to sha1 of their attributes
		elseif (is_object($id_data) && in_array('CModel',class_parents(get_class($id_data)))) {
			return get_class($id_data) . "-" . sha1(json_encode($id_data->attributes));
		}
	// json_encode won't handle non-iterateable objects
	// use print_r for those
		elseif (is_object($id_data)) {
			return get_class($id_data) . "-" . sha1(print_r($id_data, true));
		}
	// Everything else is sha1 of their print_r output
		else {
			return sha1(print_r($id_data, true));
		}
	}

	/**
	 * Converts mixed first argument into valid string ID for {@link CBaseController::beginCache}, then calls super.
	 *
	 * @var mixed $id_data Any data that {@link getHashedID} can turn into a hash string
	 * @var array $properties Properties passed along to {@link CBaseController::beginCache}
	 * @return boolean (passed through) whether we need to generate content for caching. False if cached version is available.
	 */
	public function beginCache($id_data, array $properties = array()) {
		$id = $this->getHashedID($id_data);
		return parent::beginCache($id, $properties);
	}
}