Riemann-Roch theorems via deformation quantization, I

We deduce the Riemann Roch tape formula expressing the microlocal Euler class of a perfect complex of L-modules in terms of the Chern character of the associated symbol complex and the Todd class of the manifold from the Riemann-Roch type theorem for periodic cyclic cocycles of a symplectic deformation quantization, The proof of the latter is contained in the Sequel to this paper. (C) 2002 Elsevier Science (USA).