Existence of a bounded-degree twisted group algebra for a nondegenerate grading

Let $W$ be an algebra over an algebraically closed field $F$ of characteristic zero satisfying a polynomial identity of degree $n$. Suppose that $W$ is nondegenerately graded by a group $G$. A twisted group algebra $F^{\alpha}G$ is determined by a cohomology class $\alpha\in H^2(G,F^*)$. The conjecture states that there exists a class

$$\alpha\in H^2(G,F^*)$$

such that the PI degree of $F^{\alpha}G$ is bounded by the same integer $n$. This is posed as a conjectural relationship between a nondegenerate grading of a PI-algebra and the PI degree of an associated twisted group algebra; the supplied text gives no resolution.