Is it possible to embed a YouTube video for mobile devices in a page, rather than linking to YouTube

The proper way to do it seems to be like so:

<iframe class="youtube-player" type="text/html" width="640" height="385" 
src="http://www.youtube.com/embed/VIDEO_ID" frameborder="0">
</iframe>

Check out the Youtube blog or that other blog post.

Now you only need to find a way to figure out which width and height to use for each device.

here you go, sir:

        protected var loader:Loader = new Loader();
        [Bindable]
        protected var player:Object;

        protected function view1_creationCompleteHandler(event:FlexEvent):void
        {
            trace("init")
            Security.loadPolicyFile("http://www.youtube.com/crossdomain.xml");
            loader.contentLoaderInfo.addEventListener(Event.INIT, onLoaderInit);

            loader.load(new URLRequest("http://www.youtube.com/apiplayer?version=3&enablejsapi=1"));
        }

        protected function onLoaderInit(event:Event):void {
            trace("onLoader")
            loader.content.addEventListener("onReady", onPlayerReady);
            loader.content.addEventListener("onError", onPlayerError);
            loader.content.addEventListener("onStateChange", onPlayerStateChange);
            loader.content.addEventListener("onPlaybackQualityChange", 
                onVideoPlaybackQualityChange);
        }

        public function loadVideo(id:String):void{
            player.cueVideoByUrl(id);
            trace("playing",id)
            player.playVideo();
        }

        protected function onPlayerReady(event:Event):void {
            player = loader.content;
            //player.setSize(240, 210);

            swfLoader.autoLoad = true;
            swfLoader.scaleContent = true;
            swfLoader.maintainAspectRatio = true;
            swfLoader.load(player);
            trace("theLo" ,String(data))
            loadVideo(String(data))// kell az 1-es feladathoz itt
        }

        protected function swfLoader_securityErrorHandler(event:SecurityErrorEvent):void {
            trace("securityerror",event);
        }

        protected function onPlayerError(event:Event):void {
            trace("player error:");
        }

        protected function onPlayerStateChange(event:Event):void {
            trace("player state:", Object(event).data);
        }

        protected function onVideoPlaybackQualityChange(event:Event):void {
            trace("video quality:", Object(event).data);
        }

    ]]>
</fx:Script>
<s:SWFLoader id="swfLoader" x="0" y="64" width="100%" height="100%"
             securityError="swfLoader_securityErrorHandler(event)"/>

as you see, you dont need to embed html. you can add sliders and buttons as well.. for more information, see youtube actionscript api: https://developers.google.com/youtube/flash_api_reference