Adobe hasn't officially ported Adobe AIR to Linux yet, but Ubuntu Unleashed figured out that you can install AIR using the WINE windows emulation layer for Linux. Installation isn't exactly painless, and when all is said and done, there are a bunch of AIR applications that won't run. But some will.
Note that the instructions at Ubuntu Unleashed tell you how to install Adobe AIR beta 3. But read on and we'll show you how to install Adobe AIR 1.0.
First up, you want to make sure WINE is installed. The newer the version, the better. So while you could install WINE from the Ubuntu repositories, we didn't have much success installing AIR applications. So we'd recommend following the instructions at WineHQ for adding a repository that will let you install the latest version of WINE, currently 0.9.57.
Next, you need to download and install Adobe AIR. Unfortunately, when you visit the Adobe AIR download site using Firefox, the page will detect that you're running Linux and will refuse to offer you a download link. We got around this by downloading the Opera web browser for Windows, installing it with WINE, and then visiting the Adobe AIR download page with Opera.
Once AIR is installed, you can download and install AIR applications in one of two ways. You can download the .AIR files to your computer and open them with the Adobe AIR Installer.exe file located in your /home//.wine/drive_c/Program Files/Common Files/Adobe AIR/Versions/1.0/ directory. Or if you continue using Opera or your Windows browser of choice to find your applications, you may have some luck installing them directly from the web.
We tested some of our favorite applications and found that while they all appeared to install correctly, only a handful are actually usable.