A Riemann-Roch Theorem for dg Algebras

Given a smooth proper dg algebra A, a perfect dg A-module M and an endomorphism f of M, we define the Hochschild class of the pair (M,f) with values in the Hochschild homology of the algebra A. Our main result is a Riemann-Roch type formula involving the convolution of two such Hochschild classes.