  This is the second in a sequence of papers in which we construct a quantum
version of the Kirwan map from the equivariant quantum cohomology of a smooth
polarized complex projective variety with the action of a connected complex
reductive group to the orbifold quantum cohomology of its geometric invariant
theory quotient, and prove that it intertwines the genus zero gauged
Gromov-Witten potential with the genus zero Gromov-Witten graph potential. In
this part we construct virtual fundamental classes on the moduli spaces used in
the construction of the quantum Kirwan map and the gauged Gromov-Witten
potential.
