We describe the pushforward of a matrix factorization along a ring morphism in terms of an idempotent defined using relative Atiyah classes, and we use this construction to study the convolution of kernels defining integral functors between categories of matrix factorizations. We give an elementary proof of a formula for the Chern character of the convolution generalizing the Hirzebruch–Riemann–Roch formula of Polishchuk and Vaintrob.
Tobias Dyckerhoff. Daniel Murfet. "Pushing forward matrix factorizations." Duke Math. J. 162 (7) 1249 - 1311, 15 May 2013. https://doi.org/10.1215/00127094-2142641