Cannon's conjecture on hyperbolic groups with two-sphere boundary

Let $G$ be a Gromov hyperbolic group whose boundary at infinity is homeomorphic to the two-sphere $\mathbb{S}^2$. A group is virtually Kleinian if, up to a finite-index subgroup, it can be realized as a group of discrete, cocompact isometries of real hyperbolic three-space $H^3_{\mathbb{R}}$. Cannon's conjecture. If $\partial_\infty G$ is homeomorphic to $\mathbb{S}^2$, then $G$ is virtually Kleinian. This is the two-dimensional boundary case of the relationship between the large-scale geometry of hyperbolic groups and geometric actions on real hyperbolic space; the conjecture remains open.