  We establish a geometric interpretation of orientifold Donaldson-Thomas
invariants of $\sigma$-symmetric quivers with involution. More precisely, we
prove that the cohomological orientifold Donaldson-Thomas invariant is
isomorphic to the rational Chow group of the moduli space of $\sigma$-stable
self-dual quiver representations. As an application we prove that the Chow
Betti numbers of moduli spaces of stable $m$-tuples in classical Lie algebras
can be computed numerically. We also prove a cohomological wall-crossing
formula relating semistable Hall modules for different stabilities.
