I'm using version 7.1.2 of Crossover Games for Linux.
Delta Force: Black Hawk Down installs and plays. One small trick is that you have to choose "Other Installer Location" when installing it (then navigate to the AUTORUN directory and select AUTORUN.EXE). AUTORUN.BAT is the only file in the root directory and will not install the game.
I installed the game and tried playing it immediately. There was no sound. I exited and returned, the sound was there. Now, every single time I try playing, the sound is there and absolutely everything works as it should. There are no graphic glitches, no sound glitches, and I'm convinced that it looks better than when I used to play the game when it was new (probably because my computer back in the day wasn't as powerful, so I had to knock the graphics levels down - now I can play it in its full beauty).
