SpankMarvin on "Mobile Redirect with a difference."

Although it's better to have the URL being pulled from the CMS rather than hard-coded, if you must:

(This assumes the mobile URL is http://google.com)

function do_home_redirect() {

	if( wp_is_mobile() && is_front_page() ){
			header('Location: http://google.com/');
			exit;
	}

}

add_action( 'init', 'do_home_redirect' );