  Among the possible explanations for the puzzling observations of cosmic rays
above the GZK cutoff there is growing interest in the ones that represent
kinematical solutions, based either on general formulations of particle physics
with small violations of Lorentz symmetry or on a quantum-gravity-motivated
scheme for the breakup of Lorentz symmetry. An unappealing aspect of these
cosmic-ray-puzzle solutions is that they require the existence of a preferred
class of inertial observers. Here I propose a new kinematical solution of the
cosmic-ray puzzle, which does not require the existence of a preferred class of
inertial observers. My proposal is a new example of a type of relativistic
theories, the so-called "doubly-special-relativity" theories, which have
already been studied extensively over the last two years. The core ingredient
of the proposal is a deformation of Lorentz transformations in which also the
Planck scale $E_p$ (in addition to the speed-of-light scale $c$) is described
as an invariant. Just like the introduction of the invariant $c$ requires a
deformation of the Galileian transformations into the Lorentz transformations,
the introduction of the invariant $E_p$ requires a deformation of the Lorentz
transformations, but there is no special class of inertial observers. The
Pierre Auger Observatory and the GLAST space telescope should play a key role
in future developments of these investigations. I also emphasize that the
doubly-special-relativity theory here proposed, besides being the first one to
provide a solution for the cosmic-ray puzzle, is also the first one in which a
natural description of macroscopic bodies is achieved, and may find
applications in the context of a recently-proposed dark-energy scenario.
