  In this paper we study a family of algebraic deformations of regular
coadjoint orbits of compact semisimple Lie groups with the Kirillov Poisson
bracket. The deformations are restrictions of deformations on the dual of the
Lie algebra. We prove that there are non isomorphic deformations in the family.
The star products are not differential, unlike the star products considered in
other approaches. We make a comparison with the differential star product
canonically defined by Kontsevich's map.
