the study of group actions on probability measure spaces plays a central role in modern mathematics. the (generalized) neshveyev-stormer conjecture states that the group action on a probability measure space can be completely understood by studying the inclusion of the group von neumann algebra inside the group measure space construction. in my talk i shall show that the neshveyev-stormer conjecture is true for a large class of actions. this talk is based on a joint work with ionut chifan.