On the topology of real algebraic stacks

Motivated by questions arising in the theory of moduli spaces in real algebraic geometry, we develop a range of methods to study the topology of the real locus of a Deligne-Mumford stack over the real numbers. As an application, we verify in several cases the Smith-Thom type inequality for stacks that we conjectured in an earlier work. This requires combining techniques from group theory, algebraic geometry, and topology.