  We define the reflection of a random walk at a general barrier and derive, in
case the increments are light tailed and have negative mean, a necessary and
sufficient criterion for the global maximum of the reflected process to be
finite a.s. If it is finite a.s., we show that the tail of the distribution of
the global maximum decays exponentially fast and derive the precise rate of
decay. Finally, we discuss an example from structural biology that motivated
the interest in the reflection at a general barrier.
