  This is the third 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. We
also give a formula for a solution to the quantum differential equation in
terms of a localized gauged potential. These results overlap with those of
Givental, Lian-Liu-Yau, Coates-Corti-Iritani-Tseng and Ciocan-Fontanine-Kim.
