We report the results of detailed calculations of reactive, inelastic, and dissociative processes in collisions of atomic oxygen with molecular nitrogen in their respective electronic ground states. Cross sections are calculated as a function of collision energy in the range 0.001-10 eV, considering the whole rovibrational ladder. Some problems related to the vibrational energy levels of the asymptotes of 3A″ and 3A' potential energy surfaces used in this work are solved by an appropriate scaling at the level of cross sections. The results are compared with data in the literature, obtaining excellent agreement with experimental thermal data for reactive processes on a very large temperature range, and reasonable agreement with indirect dissociative data. Significant discrepancies are observed with previous reactive state-to-state results calculated on less detailed potential energy surfaces. Inelastic results are compatible with extrapolation of experimental thermal rate coefficient for temperatures higher than 4500 K but completely fail to reproduce experimental data at room temperature. The issue is discussed, indicating the reasons and possible solutions to the problem, and a resonable rate coefficient is obtained combining experimental and theoretical results in the range 300-20000 K. Complete, accurate fits are provided for both reactive and dissociative state-to-state rate coefficients to use them in applicative numerical codes concerning air kinetics.