As part of the project for the development of the exhaust gas cooling system for the modification of the M256 engine, a turbocharger was constructed in which the exhaust manifold and turbine are actively cooled by air. At the beginning of this thesis, the "downsizing" method and turbocharging are described together with an explanation of the requirement for engine operation in the stoichiometric range and how it affects the exhaust gas temperature. An overview of existing exhaust manifold designs based on the literature and review of patents is given. Exhaust manifold performances were compared and evaluated. Then an overview and review of technical solutions for exhaust gas cooling are given. Previous research by Daimler AG related to exhaust gas cooling achieved by active exhaust air cooling has been analyzed. The concept of the exhaust cooling system of the M256 engine modification is presented. As part of the project for the development of this system, a turbocharger was constructed and a detailed explanation of the exhaust manifold, the turbine of the turbocharger and the associated shells. For the exhaust cooling system to be functional, the mass flow and the air pressure drop for the cooling of the turbocharger must be within the permissible values. The mass flow and the drop in cooling air pressure for a given structure were obtained by CFD simulations. Based on the results of CFD simulations, modifications were made to the turbocharger design. Guidelines are defined for the development of turbochargers to the stage of prototype production.