  In this paper we construct non-equivalent star products on CP^n by phase
space reduction. It turns out that the non-equivalent star products occur very
natural in the context of phase space reduction by deforming the momentum map
of the U(1)-action on C^{n+1} {0} into a quantum momentum map and the
corresponding momentum value into a quantum momentum value such that the level
set, i.~e. the `constraint surface', of the quantum momentum map coincides with
the classical one. All equivalence classes of star products on CP^n are
obtained by this construction.
