Modified Bing–Borsuk conjecture for homogeneous ANR-spaces

Let $X$ be a locally compact homogeneous $ANR$-space of dimension $n$. A generalized $n$-manifold is a locally compact $n$-dimensional $ANR$-space that is a $\mathbb Z$-homology $n$-manifold.

Modified Bing–Borsuk conjecture. Every locally compact homogeneous $ANR$-space of dimension $n\geq 3$ is a generalized $n$-manifold.

This modification was suggested by Bryant. The source does not state whether it is resolved; a positive solution of the preceding conjecture would imply that the Bing–Borsuk conjecture is false for $n\geq 6$.