The coils are under the airbox ... shirley ???

Stator coils, not ignition coils.

The generator is formed from a stator and a rotor. The rotor attaches to the crank and has a set of magnets on. The rotation of these generates a 3 phase AC voltage (which increases with revs). The reg/rec then takes this AC voltage and converts it to DC, then regulates it to the charging voltage - 13 - 14.5V DC ish.

I'm sure someone who actually knows what they are on about will come along and correct or clarify the above at some stage.