Tests of Lorentz symmetry from space

Detecting ultra-high energy cosmic-ray events from space offers a unique opportunity to test Lorentz symmetry. Possible violations of special relativity at the Planck scale must be explored by examining as closely as possible the structure and time evolution of the first interactions of the event, where Planck-scale physics can directly manifest itself through the lifetimes, decays and interaction properties of the particles involved. In this energy region, quadratically deformed relativistic kinematics (QDRK) appears as a particularly appealing phenomenological model. Possible signatures of superluminal particles with positive mass and energy (superbradyons) are also discussed.