The "How to get working in Linux on 14.1.4" in Tips & Tricks didn't work for me, but I got it installed doing the following:
- Click "Install Windows Software" in Crossover
- Search for and select Origin in the program list and click "Install" without changing anything else
- Accept all popups and at the end of the install the install will tell you it failed - just click "OK" to those popups
- Navigate to ~/.cxoffice/<bottle>/drive_c/users/Public/Application Data/Origin/SelfUpdate/StagedUpdate and copy all files and folders to ~/.cxoffice/<bottle>/drive_c/Program Files/Origin
- In folder ~/.cxoffice/<bottle>/drive_c/Program Files/Origin delete Origin.exe
- In same folder rename OriginTMP.exe to Origin.exe
- Execute Origin
Now it will actually manage to show you the login screen and you can login and download the games.