The no infinite cocycle crossed-product decomposition conjecture for II$_1$ factors

Let $M$ be a separable II$_1$ factor. Let $G$ be a countably infinite group, let $(B,\tau)$ be a tracial von Neumann algebra, and let $(\sigma,c)$ be a trace-preserving cocycle action of $G$ on $B$. No infinite cocycle crossed-product decomposition conjecture. There exists a separable II$_1$ factor $M$ such that

$$M\not\cong B\rtimes_{\sigma,c}G$$

for every countably infinite group $G$, every tracial von Neumann algebra $(B,\tau)$, and every trace-preserving cocycle action $(\sigma,c)$ of $G$ on $B$.

This would strengthen the known obstruction to scalar or finite-dimensional cocycle crossed-product decompositions. The source states that its methods do not exclude infinite-dimensional $2$-cocycles, and more broadly that it remains open whether any II$_1$ factor admits no such decomposition with an infinite group.