I got a wireless Logitech K360 Keyboard and mouse M310, and they will not work on Nexus 7 2013 (Kitkat 4.4.2). I got a USB OTG adapter, of course. The setup works great on my Galaxy Nexus (Cyanogen 11 Kitkat ROM)
From my research, someone said Logitech did not support Nexus 7 2013 (???). I have tried 4 different kernels provided in this forum (Don't try Franco and Glitch, or you won't be able to get passed the boot screen. I had to remove battery and go back to stock kernel in recovery!)
I have not tried any custom ROM, not sure they will work. Anyone knows one?
Thank you for your input!