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Modeling of high energy hadronic and nuclear interactions by the QGSJET-II generator is discussed. Recent updates related to the treatment of nonlinear effects inthe interaction dynamics and to the model calibration with new LHC data are described. A special attention is devoted to the predictions of the new model version forcharacteristics of extensive air showers initiated by high energy cosmic rays. In particular, an improved description of charge exchange processes in pion collisionsis discussed and the respective enhancement of the shower muon content is analyzed

QGSJET-II: physics, recent improvements, and results for air showers