  Ultra-high-energy physics is about to enter a new era thanks to the
impressive results of experiments such as the "Large High Altitude Air Shower
Observatory" (LHAASO), detecting photons of up to $1.4\times 10^{15}$ eV (PeV
scale). These new results could be used to test deviations with respect to
special relativity. While this has been already explored within the approach of
Lorentz Invariance Violation (LIV) theories, in this work we consider, for the
first time, modifications due to a relativistic deformed kinematics (which
appear in Doubly Special Relativity, or DSR, theories). In particular, we study
the mean free path of very high-energy photons due to electron-positron pair
creation when interacting with low-energy photons of the cosmic microwave
background. Depending on the energy scale of the relativistic deformed
kinematics, present (or near future) experiments can be sensitive enough to be
able to identify deviations from special relativity.
