  We combine our results on symmetric products and second quantization with our
description of discrete torsion in order to explain the ring structure of the
cohomology of the Hilbert scheme of points on a K3 surface. This is achieved in
terms of an essentially unique symmetric group Frobenius algebra twisted by a
specific discrete torsion. This twist is realized in form of a tensor product
with a twisted group algebra that is defined by a discrete torsion cocycle. We
furthermore show that the form of this cocycle is dictated by the geometry of
the Hilbert scheme as a resolution of singularities of the symmetric product.
