The exponential law and bounded cohomology for semidirect groupoids.

Given a measured groupoid G, together with Filippo Sarti, we defined a cohomology theory which generalizes the measurable bounded cohomology of a locally compact group. In the particular case of a groupoid associated to a measure preserving action, our cohomology boils down to the usual bounded cohomology of the group with twisted coefficients. We will discuss the possible applications of this result to orbit equivalence.