Here is my setup : In the basement, a/v receiver, cable box HDTV, a projector and on the first floor a TV.
I want to split the HDMI signal from my HDTV cablebox to my projector and TV. I know I'll have to watch the same thing on both, but will it work ? And how will I change channels on the TV if it use an infrared remote ?
You need to research ir extenders or repeaters. That would be one option.
You may also want to look at a slingbox it might be more expensive than the IR route but it will interface with a tablet or smart phone to allow you to change channels. Plus you will also get remote viewing options.