  We introduce the notion of a Bredon-style equivariant coarse homology theory.
We show that such a Bredon-style equivariant coarse homology theory satisfies
localization theorems and that a general equivariant coarse homology theory can
be approximated by a Bredon-style version. We discuss the special case of
algebraic and topological equivariant coarse $K$-homology and obtain the coarse
analog of Segal's localization theorem.
