Cheers everyone. Yesterday I got the type cover of my surface pro 4 to work under kali.
I posted a step-by-step guide here:
https://forums.kali.org/showthread.p...-Surface-Pro-4
However, I think it should work out-of-the-box with one of the weekly kali builds that have the new kernel already included.
Maybe someone tried and can confirm that? Plus: Has anyone ever tried to get to bultin Wifi module to managed mode? That would be supersweet, but as far as I've seen, chances are slim...
Otherwise: Enjoy.