Polyethylene is a widely used polymer and a prototypical polyolefin. Understanding degradation mechanisms at the atomic scale leading to oxidation under the effect of temperature and/or irradiation is crucial for many long term applications. Here we focus on a subset of reactions belonging to the generally assumed reaction scheme and involving alkoxy radicals. We follow a theoretical approach based on density functional theory (DFT), in order to assess the role of these species, which are short lived and thus hard to detect experimentally. For every considered reaction we calculate the reaction enthalpy as well as the energy barrier and we evaluate the influence of the local atomic environment, taking advantage of a model surface of a crystalline lamella which mimicks the interface between crystalline and amorphous zones. Our results suggest that, in certain conditions, the kinetic pathway can bypass the formation of hydroperoxides. The concentrations of alkoxy and peroxy radicals during radio-oxidation, as well as their ratio, are important parameters controlling the predominance of chain-scission or crosslinking of the polymer. The data presented here constitute part of a database that can be used to set up kinetic simulations based on homogeneous chemical kinetics or Monte Carlo algorithms.