How much air is recirculated (vs. bleed air injected) in modern airliners cabin?
From an own work report, based on public web presentations for type rating and on The Boeing 737 Technical Guide by Chris Brady:


  A recirculation system reduces bleed air requirements and pack loads, by filtering cabin air and re-introducing it to the mix manifold. Approximately 25% of the cabin air is recirculated. The recirculation fan will switch off if either pack is in HIGH flow, causing a net reduction in ventilation rate of about 15%. Total ventilation rate on a 737-800 is approx 1 m3/sec


  


  A portion of the conditioned air from the left pack flows directly into the flight deck. The remainder of the left pack air, all of the right pack air, and air from the recirculation system is combined into the mix manifold. Mix manifold air is distributed to the passenger cabin through different zones, via the side-wall risers on the left and right sides of the aircraft. On ground, pre-conditioned air can be pumped directly into the mix manifold


The B737 Technical Guide further mentions that on the B757 and B767, up to 50% of cabin air is recirculated, and on the MD80 none.