  Explanations of the origin of ultra-high energy cosmic rays are severely
constrained by the Greisen-Zatsepin-Kuz'min effect, which limits their
propagation over cosmological distances. We argue that possible departures from
strict Lorentz invariance, too small to have been detected otherwise, can
affect elementary-particle kinematics so as to suppress or forbid inelastic
collisions of cosmic-ray nucleons with background photons. Thereby can the GZK
cutoff be relaxed or removed.
