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The complexity of modern hybrid powertrains poses new challenges for the optimal control concerning, on one hand, the thermal engine to maximize its efficiency, and, on the other hand, the vehicle to minimize the noxious emissions and CO2. In this context, the engine calibration has to be conducted by considering simultaneously the powertrain management, the vehicle characteristics, and the driving mission. In this work, a calibration methodology for a two-stage boosted ultra-lean pre-chamber spark ignition (SI) engine is proposed, aiming at minimizing its CO2 and pollutant emissions. The engine features a flexible variable valve timing (VVT) control of the valves and an E-compressor, coupled in series to a turbocharger, to guarantee an adequate boost level needed for ultra-lean operation. The engine is simulated in a refined 1D model. A simplified methodology, based on a network of proportional integral derivative (PID) controllers, is presented for the calibration over the whole operating domain. Two calibration variants are proposed and compared, characterized by different fuel and electric consumptions: the first one aims to exclusively maximize the brake thermal efficiency, and the second one additionally considers the electric energy absorbed by the E-compressor and drained from the battery. After a verification against the outcomes of an automatic optimizer, the calibration strategies are assessed based on pollutant and CO2 emissions along representative driving cycles by vehicle simulations. The results highlight slightly lower CO2 emissions with the calibration approach that minimizes the E-compressor consumption, thus revealing the importance of considering the engine calibration phase, the powertrain management, the vehicle characteristics, and its mission. [ABSTRACT FROM AUTHOR]