von Neumann subalgebra which is isomorphic to $R$

Question

Let $M$ be a von Neumann algebra and $N$ be the von Neumann subalgebra of $M$.

If $N$ is $*$-isomorphic to the hyperfinite type II$_1$ factor $R$. Can we conclude that $N$ is also a hyperfinite type II$_1$ factor?

Answer 1

Yes, the only II$_1$-subfactors of the hyperfinite II$_1$-factor $R$ are copies of $R$. This follows from Connes 1976 Annals' paper, where he proves that every injective II$_1$-factor is hyperfinite. So $R$ is injective, and because a $\text{II}_1$-factor has conditional expectations onto any of its subfactors, any subfactor of $R$ is injective and hence hyperfinite.