Of course, the differentiable cohomology of G ⇉ ⇉ ∗ ∗ as a Lie groupoid coincides with the standard differentiable cohomology of G as a Lie group (in particular, for discrete groups one recovers the usual group cohomology). On the other hand, for any proper Lie groupoid G ⇉ ⇉ M , one can prove that H d n ( G , E ) = 0 for every n > 0 .