  We reformulate the concept of connection on a Hopf-Galois extension
$B\subseteq P$ in order to apply it in computing the Chern-Connes pairing
between the cyclic cohomology $HC^{2n} (B)$ and $K_0 (B)$. This reformulation
allows us to show that a Hopf-Galois extension admitting a strong connection is
projective and left faithfully flat. It also enables us to conclude that a
strong connection is a Cuntz-Quillen-type bimodule connection. To exemplify the
theory, we construct a strong connection (super Dirac monopole) to find out the
Chern-Connes pairing for the super line bundles associated to super Hopf
fibration.
