  For $X$ a smooth projective variety, the quantum cohomology ring $QH^*(X)$ is
a deformation of the usual cohomology ring $H^*(X)$, where the product
structure is modified to incorporate quantum corrections. These correction
terms are defined using Gromov-Witten invariants. When $X$ is toric with the
geometric quotient description $V /\!/ T$, the cohomology ring $H^*(V /\!/T)$
also has the structure of a quantum $H^*(T)$-module. In this paper, we give a
new deformation using quasimap invariants with a light point. This defines
$H^*(T)$-module structure on $H^*(X)$ through a modified version of the WDVV
equations. Using the Atiyah-Bott localization theorem, we explicitly compute
this structure for the Hirzebruch surface of type 2. We conjecture that this
new quantum module structure is isomorphic to the natural module structure of
the Batyrev ring for a semipositive toric variety.
