  We describe all possible coactions of finite groups (equivalently, all group
gradings) on two-dimensional Artin-Schelter regular algebras. We give necessary
and sufficient conditions for the associated Auslander map to be an
isomorphism, and determine precisely when the invariant ring for the coaction
is Artin-Schelter regular. The proofs of our results are combinatorial and
exploit the structure of the McKay quiver associated to the coaction.
