The Grothendieck and Picard groups of a complete toric DM stack

We compute the Grothendieck and Picard groups of a complete smooth toric Deligne-Mumford stack by using a suitable category of graded modules over a polynomial ring.Comment: keywords: Graded rings, graded modules, toric DM stacks, Grothendieck group, Picard group. This is the final published versio