  We study the G-centers of G-graded monoidal categories where G is an
arbitrary group. We prove that for any spherical G-fusion category C over an
algebraically closed field such that the dimension of the neutral component of
C is non-zero, the G-center of C is a G-modular category. This generalizes a
theorem of M. M\"uger corresponding to G=1. We also exhibit interesting objects
of the G-center.
