The equivariant CR Yamabe conjecture

Let $(M,J,\theta)$ be a compact strictly pseudoconvex CR manifold of real dimension $2n+1$, and let $G$ be a compact subgroup of $I(M,\theta)$, the group of pseudo-Hermitian transformations preserving the associated contact Riemannian metric. A contact form is conformal to $\theta$ if it is obtained from $\theta$ by conformal rescaling, and it is $G$-invariant when it is preserved by the action of $G$. Equivariant CR Yamabe conjecture. There exists a $G$-invariant contact form conformal to $\theta$ whose Webster scalar curvature is constant. This is the equivariant version of the CR Yamabe problem, introduced to seek constant Webster scalar curvature within a symmetry class; the supplied text does not state whether the conjecture has been resolved.