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.