  The Bogomolov multiplier is a group theoretical invariant isomorphic to the
unramified Brauer group of a given quotient space. We derive a homological
version of the Bogomolov multiplier, prove a Hopf-type formula, find a five
term exact sequence corresponding to this invariant, and describe the role of
the Bogomolov multiplier in the theory of central extensions. A new description
of the Bogomolov multiplier of a nilpotent group of class two is obtained. We
define the Bogomolov multiplier within K-theory and show that proving its
triviality is equivalent to solving a long-standing problem posed by Bass. An
algorithm for computing the Bogomolov multiplier is developed.
