Tateness conjecture for motivic classes of translation quiver representation spaces

Let $Q$ be a quiver with an automorphism $\ta$, let $\bv\in\bN^{(Q_0)}$ be a dimension vector, and let $\cR^\ta(Q,\bv)$ denote the space of pairs $(M,\vi)$ with $M\in\cR(Q,\bv)$ and $\vi\in\operatorname{Hom}(M,M^\ta)$. Tateness conjecture. The motivic class of $\cR^\ta(Q,\bv)$ is Tate. This conjecture predicts that these motivic classes lie in the Tate subring of the relevant Grothendieck ring; the supplied text does not state any cases in which the claim is proved or refuted.