  GRB X-ray light curves display rapid declines followed by a gradual
steepening or plateau phase in >~ 30% of GRBs in the Swift sample. Treating the
standard relativistic blastwave model in a uniform circumburst medium, it is
shown that if GRBs accelerate ultra-high energy cosmic rays through a Fermi
mechanism, then the hadronic component can be rapidly depleted by means of
photopion processes on time scales ~100 - 10^4 s after the GRB explosion. While
discharging the hadronic energy in the form of ultra-high energy cosmic ray
neutrals and escaping cosmic-ray ions, the blast wave goes through a strongly
radiative phase, causing the steep declines observed with Swift. Following the
discharge, the blast wave recovers its adiabatic behavior, forming the observed
plateaus or slow declines. These effects are illustrated by calculations of
model bolometric light curves. The results show that steep X-ray declines and
plateau features occur when GRB sources take place in rather dense media, with
n >~ 100 cc out to >~ 10^17 cm.
