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Umm, how do you propose to remove all nitrogen from the air going into the engine? N2 is roughly 70% of what goes into the engine to start with. Even after adding hydrocarbons and then combusting them, you'll still have around 70% of it is nitrogen of one form or another, mostly N2.
Just routing exhaust gas (cooled or not) into the intake won't substantially change the amount of N2 going through the system, since you'll be displacing 70% N2 air with 70% N2 exhaust.
If you could eliminate NOx, that would enable lean mixtures for good fuel economy. But it's hard to see how this would accomplish it.
-soD
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