Let G be a connected reductive group with maximal torus T, and let V and E be two representations of G. Then E defines a vector bundle on the orbifold V//G; let X//G be the zero locus of a regular section. The quasimap I-function of X//G encodes the geometry of maps from P^1 to X//G and is related to Gromov-Witten invariants of X//G. By directly analyzing these maps from P^1, we explain how to relate the I-function of X//G to that of V//T. In joint work with Nawaz Sultani, we use our formulas to validify a mirror symmetry computation of Oneto-Petracci that relates the quantum period of X//G to a certain Laurent polynomial defined by a Fano polytope.