video playback to TV?

can I playback video from my iPod Touch to my HDTV via wifi? I was able to share downloaded videos from my Nexus 7 and my dad's Windows 8.1 PC, but I can't find a solution that will work as well as it did on android. any suggestions? I know that Apple sells a composite AV cable, but that's not true HD, and there is no lightning cable support either, so I was wondering what the work around would be? I want to be able to watch content from apps on my HDTV in Tahoe Donner, and been looking into this issue for a few years with no solution... please help!