I use Motul Scooter Power 4T 5W40; the previous fill was Motul 300V 5W50 -- really expensive and I doubt my better half hammers her Downtown 300i on the track.
I'd probably put regular Castrol 80W90 in the final drive unit though and save some money. I don't think there's as much advantage to having fully synthetic oil in the final drive than in the engine crankcase. There are no combustion byproducts to deal with, and the high molybdenum content in the oil probably protects the final drive gears just fine.
