Computation of a closed star-product invariant on a symplectic manifold

Let M be a symplectic manifold over R. In [CFS] the authors construct an in variant phi in the cyclic cohomology of M for any closed star-product, They compute this invariant in the de Rham complex of M when M = T*V. We genera lize this result by computing the image of phi in the de Rham complex for a ny symplectic manifold and any star-product and we show how this invariant is related to the general classification of Kontsevich. The proof uses the Riemann-Roch theorem for periodic cyclic chains of Nest-Tsygan.