the AVR-888 which in turn is wirelessly connected to my DVD, Projector, Cablebox etc.
you have wireless connections! how does that work?
OK, I am assuming you want to go from the AVR 888 via an HDMI cable to your display, right? The AVR 888 will convert analog video to HDMI output.... the problem is that it will NOT do it with 1080p video. Honestly, if you have a spare HDMI input on the 888 I would just grab an HDMI cable (under 10 bucks from monoprice) and call it a day.
But, here's how you do it with component (RGB) cables. What you want to do is hook up the Xbox 360 via the component cable (plus an optical audio cable for digital audio) into a spare input on the Denon.
Then, the critical step is you need to find an unused "name" like "VCR" or "HDP" or something, and then ASSIGN THE INPUTS you used to that name. For example, if you plugged into the Component #2 spot and Optical #1, and you want to use "VCR", you would need to go to the INPUT SETUP menu, select "VCR" at the top, and then go to ASSIGN and set it to "RCA-2" and "OPT-1" and everything else to "None". You can of course rename it to say "XBOX 360" instead of "VCR". Then, when you select the "VCR" input, it will say "XBOX 360" on the display and it will use the video from comp #2 and the audio from opt #1. (If you don't have an optical cable and are just going to use the red/white analog audio for now, make sure to plug it into the same name you just used, e.g. "VCR" inputs, or else it won't match up).
Now, the final step relates to what I said above: the Denon will NOT convert component video that is 1080p. So you need to set the Xbox 360 to output at a lower resolution (720p or 1080i) and then it will output over HDMI to your display.