  We consider the process of collision between a hard photon and a soft photon
producing an electron-positron pair, under the assumption that the kinematics
be described according to the $\kappa$-deformation of the D=4 Poincar\'{e}
algebra. We emphasize the relevance of this analysis for the understanding of
the puzzling observations of multi-TeV photons from Markarian 501. We find a
significant effect of the $\kappa$-deformation for processes above threshold,
while, in agreement with a previous study, we find that there is no
leading-order deformation of the threshold condition.
