Characteristic-invariant conjecture for almost periodic actions on the hyperfinite type II_1 factor

Let $G$ be the acting group and let $R$ be the hyperfinite type $\mathrm{II}_1$ factor. Let $\alpha:G\curvearrowright R$ be an almost periodic action such that $R\rtimes_\alpha G$ is a factor. Define

$$H=\{h\in G\mid \alpha_h\in\operatorname{Inn}(R)\}$$

and, for $h\in H$, choose $v\in\mathcal{U}(R)$ with $\operatorname{Ad}(v)=\alpha_h$. The associated bicharacter is $\chi:G\times H\to\mathbb{T}$, defined by $\chi(g,h)=\alpha_g(v)v^*$.

Characteristic-invariant conjecture. The action $\alpha$ is classified up to cocycle conjugacy by the characteristic invariant $(H,\chi)$.

The source identifies this as the remaining case in the classification of almost periodic actions on the hyperfinite type $\mathrm{II}_1$ factor when the crossed product is a factor but the action is not outer. The status of this classification problem is not resolved in the supplied text.