It is conjectured that for a discrete, finitely presented group $G$ such that $BG$ satisfies Poincaré duality, there actually exists a closed manifold $M$ which is homotopy equivalent to $BG$.
This is somehow pointing in the opposite direction as Borel's conjecture, which implies that the homeomorphism type of such a manifold $M$ is uniquely determined.
Who conjectured this first? Is it also due to Borel, or was it Wall, or somebody else?