Neighborhood equivariant retract conjecture for twisted products

Let $G$ be a locally compact group, let $K$ be a compact large subgroup of $G$, and let $S$ be a $K$-space. The neighborhood equivariant retract conjecture. $S$ is a neighborhood $K$-equivariant retract of the twisted product $G\times_K S$. This would extend the preceding retract results for orbit spaces and provide an extension property for proper group actions; the source does not state a resolution of the conjecture.