  We prove that every finitely generated group with recursive aspherical
presentation embeds into a group with finite aspherical presentation. This and
several known facts about groups and manifolds imply that there exists a
4-dimensional closed aspherical manifold $M$ such that the fundamental group
$\pi_1(M)$ coarsely contains an expander, and so it has infinite asymptotic
dimension, is not coarsely embeddable into a Hilbert space, and does not
satisfy the Baum-Connes conjecture with coefficients. Closed aspherical
manifolds with any of these properties were previously unknown.
