  We discuss the possibility of explaining the observation of ultra-high-energy
cosmic rays with energy above the GZK cutoff, saving the relativity principle
and the (possibly deformed) Lorentz symmetry, as proposed recently by several
authors. Since it is known that the Lie group structure of the Lorentz group
cannot be deformed, we study the deformations (up to isomorphisms) of the
mass-shell, considered as an abstract three-dimensional homogeneous space. We
find that in the massive case the mass-shell cannot be deformed and in the
massless case there are deformations, but their physical interpretation is
problematic. The components of the four-momentum are considered as (redundant)
coordinates on the abstract mass-shell. Reinterpreting an old result, we note
that if the four-momentum is conserved its components must be the usual ones,
with linear Lorentz transformation properties. Even if four-momentum is not
conserved at high center-of-mass energies, the linearly transforming
coordinates can always be used to describe in a convenient way the kinematics
of collision processes and they satisfy the GKZ cutoff. We suggest that, if one
wants to save the relativity principle, one should look for new physics in the
collisions between the ultra-high-energy cosmic rays and the nuclei of the high
atmosphere.
