  We enlarge the category of bornological coarse spaces by adding transfer
morphisms and introduce the notion of an equivariant coarse homology theory
with transfers. We then show that equivariant coarse algebraic $K$-homology and
equivariant coarse ordinary homology can be extended to equivariant coarse
homology theories with transfers. In the case of a finite group we observe that
equivariant coarse homology theories with transfers provide Mackey functors. We
express standard constructions with Mackey functors in terms of coarse
geometry, and we demonstrate the usage of transfers in order to prove
injectivity results about assembly maps.
