public function init()
{
    $username = craft()->request->getQuery('username');

    if ($username)
    {
        craft()->urlManager->setRouteVariables(array(
            'username' => $username
        ));

        craft()->runController('myPluginHandle/myPluginActionMethod');
    }
}

class MyPluginController extends BaseController
{
    protected $allowAnonymous = true;

    public function actionDoIt($username)
    {
        // Do your thing.

        $this->redirect('homepage');
    }
}