We are wanting to use the SharePoint app on our company owned Android tablets and not going directly to the site. I noticed, in the app, that I cannot download any file (PDF, Word doc, etc) from a document library. If I click the vertical ellipses mark I can only open or share. Opening the file still doesn't show any other options, but if I open the file with the Office app or Adobe Reader it then lets me save it. I'm a global admin, and to my knowledge, there isn't any CA's or App restriction policies to disallow me from saving it to the device. I can't even save it to my OneDrive.
