Cyclic cohomology of etale groupoids J.-L. Brylinski ∗ Department of Mathematics 305 McAllister The Pennsylvania State University University Park, PA 16802 Victor Nistor † Harvard University Department of Mathematics One Oxford Street Cambridge, MA 02138 June 20, 2003 Abstract We extend Connes’s computation of the cyclic cohomology groups of smooth algebras arising from foliations with separated graphs. We find that the characteristic classes of foliations factor through these groups. Our results also explain some results of Atiyah and Segal on orbifold Euler characteristic in the setting of cyclic homology. Contents 1 Introduction 2 2 Smooth groupoids and their convolution algebras 3 3 A reduction to loops 8 4 A simplicial resolution 12 5 The main results 20 * Partially supported by NSF grants DMS 92-03517 and DMS 89-03248 † Partially supported by NSF grant DMS 92-05548 1