The Keel-Mori theorem is a fundamental result that asserts that every separated Deligne-Mumford stack has a coarse moduli space. We will discuss a generalization of this theorem to algebraic stacks with possibly infinite stabilizer groups, and we will apply this generalization to construct projective moduli spaces parameterizing Bridgeland semistable objects on a K3 surface. This is joint work with Daniel Halpern-Leistner and Jochen Heinloth.