Actually, there
is an amazing piece of software called
Wine which implements a good portion of the Windows API, so that many Windows programs can, in fact, run.
Linux also offers, through its XWindows/XOrg subsystems
(no relation to "Microsoft Windows"), the ability to efficiently run remote sessions without resorting to crap like "Remote Desktop." (It is actually a
client/server graphic model, where the two computers exchange drawing commands, not bitmaps.)
However – I suggest that you should
very soberly assess exactly what use-case you are dealing with and what is the best-all-around way to meet these
business objectives. It may well be that Microsoft Windows
is the best platform for your purposes, and "Redmond came by their immense fortunes quite honestly."