VIC-modules over noncommutative rings

For a finite ring $R$, not necessarily commutative, we prove that the category of $text{VIC}(R)$-modules over a left Noetherian ring $mathbf{k}$ is locally Noetherian, generalizing a theorem of the authors that dealt with commutative $R$. As an application, we prove a very general twisted homology stability for $text{GL}_n(R)$ with $R$ a finite noncommutative ring.