  Given a finite group G acting as automorphisms on a ring A, the skew group
ring A*G is an important tool for studying the structure of G-stable ideals of
A. The ring A*G is G-graded, i.e.G coacts on A*G. The Cohen-Montgomery duality
says that the smash product A*G#k[G]^* of A*G with the dual group ring k[G]^*
is isomorphic to the full matrix ring M_n(A) over A, where n is the order of G.
In this note we show how much of the Cohen-Montgomery duality carries over to
partial group actions in the sense of R.Exel. In particular we show that the
smash product (A*_\alpha G)#k[G]^* of the partial skew group ring A*_\alpha G
and k[G]^* is isomorphic to a direct product of the form K x eM_n(A)e where e
is a certain idempotent of M_n(A) and K is a subalgebra of (A *_\alpha
G)#k[G]^*. Moreover A*_\alpha G is shown to be isomorphic to a separable
subalgebra of eM_n(A)e. We also look at duality for infinite partial group
actions and for partial Hopf actions.
