Baum-Dąbrowski-Hajac topological Borsuk-Ulam conjecture

Let $X$ be a compact Hausdorff space with a free action of a nontrivial compact group $G$. Equip the join $X * G$ with the diagonal action. Baum-Dąbrowski-Hajac's topological Borsuk-Ulam conjecture. There is no equivariant map

$$X * G \to X.$$

This generalizes the Borsuk-Ulam theorem from antipodal actions on spheres to free actions of compact groups on compact Hausdorff spaces. The source gives no resolution status for this conjecture.