This makes me wonder whether it would be theoretically possible to use some of the engine's power output to extract nitrogen from the incoming air. You'd effectively be trading more CO2 pollution (because of the reduced efficiency) for less NOx pollution.

My back-of-the-envelope calculations suggest that off-the-shelf oxygen concentrators aren't efficient enough to make this practical, but I don't know whether there are fundamental thermodynamic limits that would prevent the efficiency from being improved.