Weak factorization and the Grothendieck group of Deligne–Mumford stacks

We construct a presentation for the Grothendieck group of Deligne–Mumford stacks over a field of characteristic zero. The generators for this presentation are smooth, proper Deligne–Mumford stacks and the relations are expressed in terms of stacky blow-ups. In the process we prove a version of the weak factorization theorem for Deligne–Mumford stacks.