"Android OS" is continuously downloading something in the background, how can I stop that?
I've found the culprit! I went to Settings > Call > Internet call settings and deleted the SIP account I had once created and forgot. The phone kept reaching the SIP server (probably to check for incoming calls).

I had to install a packet sniffer on the phone (tPacketCapture) to see where the requests where going and realize I had configured a SIP account.