Equivariant quantization on quotients of simple Lie groups by reductive   subgroups of maximal rank
  We consider a class of homogeneous manifolds including all semisimple coadjoint orbits. We describe manifolds of that class admitting deformation q uantizations equivariant under the action of $G$ and the corresponding quantum group. We also classify Poisson brackets relating to such quantizations. 
Joseph Donin and Vadim Ostapenko