  We introduce group corings, and study functors between categories of
comodules over group corings, and the relationship to graded modules over
graded rings. Galois group corings are defined, and a Structure Theorem for the
$G$-comodules over a Galois group coring is given. We study (graded) Morita
contexts associated to a group coring. Our theory is applied to group corings
associated to a comodule algebra over a Hopf group coalgebra.
