Battery, stator, and rectifier/regulator. If your battery is new and holds above 12.6 volts a couple hours after being taken off of a charger, it's probably good (no guarantee).
The stators and rectifier/regulator units on these bikes go out a lot. One theory is that one part goes out and fries the other (not sure which way it works). Either way, I'd start out with a new rectifier/regulator unit from a place like
this.If that doesn't work, go for a new stator. I had good luck with a used unit from eBay, but there's always a risk that you'll get a bad part.
Search for posts by dragonfly, she had the same situation very recently.