On the algebraic index for riemannian \'etale groupoids

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian 'etale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for riemannian 'etale groupoids. We discuss solutions to that index problem when the groupoid is proper or defined by a constant Dirac structure on a 3-dim torus.