I'm afraid a simple adapter is not going to work for you. The new Apple Cinema Displays are Digital Input only. All DVI ports are not the same: some carry Digital and/or analog (DVI-I), some carry ONLY Digital (DVI-D). For example the DVI port on a Mac mini is DVI-I: it can be connected to LCD monitor through the DVI connection directly, OR it can use a simple adapter to connect to an Analog CRT monitor.
The new Apple Cinema Displays have a DVI-D input. They can only take a Digital signal. This is bad news because right now your XBox 360 can only output Analog signals: VGA, component, composite, s-video. In order to connect your Xbox 360 to your Apple display you will need a device that will convert, not just simply adapt, the signal from analog to digital DVI-D. These can be very expensive. The cheapest one I have seen is the Nyeco NCP-261D VGA/Component to DVI video converter. MSRP is $299 USD, but I have seen it in a few places for $189 USD.
http://www.digitalconnection.com/Pro...deo/dcp261.ASP
The good news: Microsoft has announced that they will be releasing a Digital HDMI cable for the XBox 360. Some believe this could happen as soon as 11/22/06 (2 days from now). With this cable, you will probably be able to use a DVI-D to HDMI adapter (a simple connector adapter) to connect your XBox 360 to your Apple Cinema Display. I hope this all made sense.
Peace.