On the algebraic index for riemannian étale groupoids

In this paper we construct an explicit quasi-isomorphism to study the cyclic cohomology of a deformation quantization over a riemannian étale groupoid. Such a quasi-isomorphism allows us to propose a general algebraic index problem for riemannian étale 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.

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