  The object of this paper is to show that non-homotopy finite Poincar\'e
duality spaces are plentiful. Let $\pi$ be finitely presented group. Assuming
that the reduced Grothendieck group $\tilde K_0(\Bbb Z[\pi])$ has a non-trivial
2-divisible element, we construct a finitely dominated Poincar\'e space $X$
with fundamental group $\pi$ such that $X$ is not homotopy finite. The
dimension of $X$ can be made arbitrarily large. Our proof relies on a result
which says that every finitely dominated space possesses a stable Poincar\'e
duality thickening.
