  We generalize Chevalley's theorem about restriction of \mathfrak{g}-invariant
polynomial functions \mathfrak{g}->C to W-invariant functions on the Cartan
\mathfrak{h}->C. We consider the case when \mathfrak{g} is replaced by a
quantum group and the target space of the polynomial maps is replaced by a
finite dimensional representation V of this quantum group. We prove that the
restriction map Res:(O_q(G)\otimes V)^{U_q(\mathfrak{g})}-> O(H)\otimes V is
injective and describe the image.
