  We consider pairs of maps from a discrete group to the unitary group. The
deficiencies of these maps from being homomorphisms may be great, but if they
are close to each other then we call such pairs balanced. We show that balanced
pairs determine elements in the K-theory group of the classifying space of the
discrete group. We also show that a Fredholm representation determines balanced
pairs.

K-Theory and Homology;Operator Algebras