Particle physics @ $\sqrt{s_{pp}}$ > 50 TeV with the Pierre Auger Observatory

Abstract: The Pierre Auger Observatory in Argentina provides the largest data sample of the cosmic ray events with energy above 10$^{18}$ eV. These high energy events can be used to test our understanding of the hadronic interactions at energies beyond the reach of colliders and to probe the basic properties of these interactions such as the inelastic cross-section of proton-air collisions. The combination of an array of surface detectors and the fluorescence telescopes of the Pierre Auger Observatory reduces significantly the dependency of the shower energy estimation on MC simulations. Despite that, the interpretation of mass sensitive quantities such as the shower maximum in terms of chemical composition of cosmic rays still depends on the hadronic interaction models. This contribution describes the main results of the observatory concerning the chemical composition of the cosmic rays and focuses on the problem of muon deficit in hadronic interaction models and on the estimation of proton-air cross-section from air-shower data.