We describe the pushforward of a matrix factorisation along a ring morphism
in terms of an idempotent defined using relative Atiyah classes, and use this
construction to study the convolution of kernels defining integral functors
between categories of matrix factorisations. We give an elementary proof of a
formula for the Chern character of the convolution generalising the
Hirzebruch-Riemann-Roch formula of Polishchuk and Vaintrob.