Noncommutative covering projections and $K$-homology

If $X$ is a topological space then there is a natural homomorphism ${\pi }_1(X)\to K_1(X)$ 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.