  In this article, the cyclic homology theory of formal deformation
quantizations of the convolution algebra associated to a proper etale Lie
groupoid is studied. We compute the Hochschild cohomology of the convolution
algebra and express it in terms of alternating multi-vector fields on the
associated inertia groupoid. We introduce a noncommutative Poisson homology
whose computation enables us to determine the Hochschild homology of formal
deformations of the convolution algebra. Then it is shown that the cyclic
(co)homology of such formal deformations can be described by an appropriate
sheaf cohomology theory. This enables us to determine the corresponding cyclic
homology groups in terms of orbifold cohomology of the underlying orbifold.
Using the thus obtained description of cyclic cohomology of the deformed
convolution algebra, we give a complete classification of all traces on this
formal deformation, and provide an explicit construction.
