Invariant von Neumann subalgebras of crossed products and tensor products

Let $Γ$ be a countable discrete group acting on a tracial von Neumann algebra $(Q,τ_Q)$ in a trace-preserving way. We study invariant von Neumann subalgebras of $Q\rtimesΓ$ and of $L(Γ)\bar\otimes Q$, where the latter is equipped with the diagonal action. We show that, under the pointwise weak mixin