Cyclic formality and index theorems - In memory of Moshe Flato

The Letter announces the following results (the proofs will appear elsewher e). An operad acting on Hochschild chains and cochains of an associative al gebra is constructed. This operad is formal. In the case when this algebra is the algebra of smooth function on a smooth manifold, the action of this operad on the corresponding Hochschild chains and cochains is formal. The i nduced map on the (periodic) cyclic homology is given by the formula involv ing the A-genus. The index theorem for degenerate Poisson structures follow s from the latter fact.