  Let F be characteristic zero field, G a residually finite group and W a
G-prime and PI F-algebra. By constructing G-graded central polynomials for W,
we prove the G-graded version of Posner's theorem. More precisely, if S denotes
all non-zero degree e central elements of W, the algebra S^{-1}W is G-graded
simple and finite dimensional over its center.
  Furthermore, we show how to use this theorem in order to recapture the result
of Aljadeff and Haile stating that two G-simple algebras of finite dimension
are isomorphix iff their ideals of graded identities coincide.
