  We show the existence of a natural Dirichlet-to-Neumann map on Riemannian
manifolds with boundary and bounded geometry, such that the bottom of the
Dirichlet spectrum is positive. This map regarded as a densely defined operator
in the $L^2$-space of the boundary admits Friedrichs extension. We focus on the
spectrum of this operator on covering spaces and total spaces of Riemannian
principal bundles over compact manifolds.
