  If $X$ is a topological space then there is a natural homomorphism
$\pi_1(X)\rightarrow K_1(X)$ from a fundamental group to a $K_1$-homology
group. Covering projections depend of fundamental group. So $K_1$-homology
groups are interrelated with covering projections. This article is concerned
with a noncommutative analogue of this interrelationship.
