Given a Lie group G, Bott proved the formula $H^p(\Omega^q(G_{\bullet}))\cong H^{p-q}(G,S^q({\cal g}^*))$, relating the cohomology of the classifying space BG to the representations in the polynomials in the Lie algebra. I the talk I intend to describe how the same formula holds true for general Lie groupoids, provided one works in the context of representations up to homotopy. If time permits, I will explain how this fomula relates to the models of Getzler and Cartan for equivariant cohomology and also describe some combinatorics which are involved in the construction of tensor products of representations up to homotopy. This is joint work with M. Crainic and B. Dherin.