UPS not going to work. Wattage-wise, the pellet stove pulls around 650 watts with the ignitor running - otherwise, around 255 watts continous. That amount of power will have a deep cycle marine battery, using an inverter, dead within a half hour, and within minutes if it has to use the ignitor.
The formula is Amps = Watts/Volts. A 400 watt inverter for your car will draw 33.3 amps @ 12 volts IF it converted perfectly. That means, you need a lot more than a cigarette lighter inverter, those are on a 15 amp fuse. This inverter would need to be directly hooked to your car battery. I didn't see any inverter above 400 watts continous, the most I've seen is
http://www.etronics.com/product.asp?stk_code=pylpinv3&store;=&catid=5752 which is 800 watts high surge, and 400 watts continous. That's in a perfectly controlled lab, don't expect it to meet that in real life conditions but at least it's closer to your mark. It's the only thing that may have a chance of working I feel, besides a generator. Use an extension cord rated to handle 650 watts or 6 amps.