Given a weakly compact action (Ozawa-Popa) of a discrete group \Gamma$\Gamma$ on p.m space X$X$, consider the Koopman representation \pi$\pi$ on L^2(X)$L^2(X)$. Compose this representation with the Calkin projection. Will the resulting representation of \Gamma$\Gamma$ be weakly contained in the left regular representation of the group, perhaps under suitable conditions?