In the interest of having the information here in case someone stumbles upon this, it is important to note that the solution varies depending on the CakePHP version.
For CakePHP 1.1
$this->renderElement('display', array('flag' => 'value'));
in your view, and then in /app/views/elements/ you can make a file called display.thtml, where $flag will have the value of whatever you pass to it.
For CakePHP 1.2
$this->element('display', array('flag' => 'value'));
in your view, and then in /app/views/elements/ you can make a file called display.ctp, where $flag will have the value of whatever you pass to it.
In both versions the element will have access to all the data the view has access to + any values you pass to it. Furthermore, as someone pointed out,
requestAction() is also an option, but it can take a heavy toll in performance if done without using cache, since it has to go through all the steps a normal action would.