I´ll discuss work in progress on determination of the ring structure of the quantum cohomology of a toric variety X with values in an (omalous) bundle V. The multiplication on quantum cohomology is defined in terms of an integral over the GLSM moduli space, a particular compactification of the space of maps from a curve to X. For toric X, this compactification is itself toric. An important part of the problem is therefore to determine the ring structure on classical coherent sheaf valued cohomology of a toric variety.