When I try to install a game from Lutris, Itch, or Steam on my desktop, I get an error message saying that I don't have permission to install programs on the desktop. I've tried several methods, but none of them have worked.
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Did You do what is mentioned on the Window? Are Lutris and Steam installed as Flatpak or .deb/APT Package? When they should be Flatpaks, I would suggest to try the .deb Versions instead.