Fusion of twisted representations

The comultiplication formula for fusion products of untwisted representations of the chiral algebra is generalized to include arbitrary twisted representations. We show that the formulae define a tensor product with suitable properties, and determine the analogue of Zhu's algebra for arbitrary twisted representations. As an example we study the fusion of representations of the Ramond sector of the N = 1 and N = 2 superconformal algebra. In the latter case, certain subtleties arise which we describe in detail.