we investigate some structural properties of c*-algebras generated by quasi-regular representations of stabilizers of boundary actions of discrete groups g. our main tool is the notion of (noncommutative) boundary maps, namely g-equivariant unital positive maps from g-c*algebras to c(b), where b is the furstenberg boundary of g. we completely describe the tracial structure and characterize the simplicity of these c*-algebras. as an application, we show that the c*-algebra generated by the quasi-regular representation associated to thompson's groups $f < t$ does not admit traces and is simple. \\ \\ this is joint work with eduardo scarparo.