  We consider gauged linear sigma models (GLSM) on $\mathbb{RP}^2$, obtained
from a parity projection of $S^2$. The theories admit squashing deformation,
much like GLSM on $S^2$, which allows us to interpret the partition function as
the overlap amplitude between the vacuum state and crosscap states. From these,
we extract the central charge of Orientifold planes, and observe that the Gamma
class makes a prominent appearance as in the recent D-brane counterpart. We
also repeat the computation for the mirror Landau-Ginzburg theory, which
naturally brings out the $\theta$-dependence as a relative sign between two
holonomy sectors on $\mathbb{RP}^2$. We also show how our results are
consistent with known topological properties of D-brane and Orientifold plane
world-volumes, and discuss what part of the wrapped D-brane/Orientifold central
charge should be attributed to the quantum volumes.
