  We consider a 2D Schroedinger operator H0 with constant magnetic field, on a
strip of finite width. The spectrum of H0 is absolutely continuous, and
contains a discrete set of thresholds. We perturb H0 by an electric potential V
which decays in a suitable sense at infinity, and study the spectral properties
of the perturbed operator H = H0 + V . First, we establish a Mourre estimate,
and as a corollary prove that the singular continuous spectrum of H is empty,
and any compact subset of the complement of the threshold set may contain at
most a finite set of eigenvalues of H, each of them having a finite
multiplicity. Next, we introduce the Krein spectral shift function (SSF) for
the operator pair (H,H0). We show that this SSF is bounded on any compact
subset of the complement of the threshold set, and is continuous away from the
threshold set and the eigenvalues of H. The main results of the article concern
the asymptotic behaviour of the SSF at the thresholds, which is described in
terms of the SSF for a pair of effective Hamiltonians.
