Although Adobe AIR is no longer maintained, there are some previous versions still available for download if you need Adobe AIR for installing an application on Pardus.
I stumbled upon a previous blogpost in turkish (of course

) on how to install Adobe AIR in Pardus, then I found the author on Google+ and asked him if he was able to and willing to translate that howto in english.
Here is his reply, for any of you who might need Adobe AIR although discontinued by Adobe itself:
Many thanks to the author, Anıl Özbek !
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Adobe Air on Pardus
Hi all Pardusers,
This is a shortened translation of Pardusta Adobe Air ve Tweetdeck Çalıştırmak (Running Adobe AIR and Tweetdeck on Pardus) [1]. I wrote this document because some Pardus users need (and ask from me) something like that. Currently I don't use Adobe AIR so I can't help more. It has been almost four years [2].
Let's start:
1. First we need to install Adobe AIR SDK:
http://airdownload.adobe.com/air/lin/download/latest/AdobeAIRSDK.tbz22. Now create a directory that named air-sdk.
2.5. Copy the archive file to this folder.
3. Extract the downloaded archive to air-sdk directory via context menu.
4. Open Dolphin with authorized user rights via kdesu dolphin command.
5. Copy air-sdk directory to /opt
6. Give executable file permissions to /opt/air-sdk/bin/adl via chmod +x /opt/air-sdk/bin/adl command or context menu. You can skip this step if these rights are already given.
7. Create a shortcut for future convenience in /usr/bin. For this you can use Dolphin or ln -s /opt/air-sdk/bin/adl /usr/bin/air command.
8. Now test time. Download an Adobe AIR application. For example Tweetdeck:
http://www.mediafire.com/?5dblnlg2r2unv7g9. Extract the *.air file with Ark.
10. Copy tweetdeck directory to /opt/air-sdk
11. And finally we can runnnnnn: air -nodebug /opt/air-sdk/tweetdeck/META-INF/AIR/application.xml /opt/air-sdk/tweetdeck
No proofread, have fun

Regards,
Anıl. (
https://plus.google.com/u/0/113435503145887565355/posts )
[1]
http://vedatfetah.blogspot.com/2011/12/pardusta-adobe-air-ve-tweetdeck.html[2]
http://anilozbek.blogspot.com/2008/11/pardusta-adobe-air.html