The notion of Strong Approximate Transitivity (SAT) for group actions on probability measure spaces was introduced by Jaworski in the early 90's. A canonical example of an SAT group action is provided by a group acting on its Poisson boundary (with respect to some "nice" probability measure on the group).   
In this talk, I will discuss a noncommutative analogue of the SAT property, and its connection with noncommutative Poisson boundary inclusions.