  We construct an equivariant version of discrete Morse theory for simplicial
complexes endowed with group actions. The key ingredient is a 2-categorical
criterion for making acyclic partial matchings on the quotient space compatible
with an overlaid complex of groups. We use the discrete flow category of any
such compatible matching to build the corresponding Morse complex of groups.
Our main result establishes that the development of the Morse complex of groups
recovers the original simplicial complex up to equivariant homotopy
equivalence.
