Beginning June 14 2011, Adobe AIR is no longer supported for desktop Linux distributions.
What is Adobe AIR ?
Adobe AIR will run on Microsoft Windows, Apple's IOS, Google Android, and on smart TVs but no longer in Linux.
The last version to support desktop Linux distributions is AIR 2.6. This means, applications compiled using AIR 2.6 and earlier will run on Linux. However, you won't be able to install Adobe AIR software compiled using AIR 2.7+ in Linux. (Reasons for discontinuing Linux support is given here).
Linux developers who are still interested in developing software using Adobe AIR can download version 2.6 AIR SDK for Linux from the AIR Archive.