A method and system are described for on-board treatment of an exhaust stream containing CO2 emitted by a hydrocarbon-fueled internal combustion engine (ICE) used to power a vehicle in order to reduce the amount of CO2 discharged into the atmosphere which include: a. a treatment zone on board the vehicle containing a capture agent having a predetermined capacity for extracting CO2 from the exhaust stream, the treatment zone preferably operating in swing mode with at least two subsystems, each having an inlet for admitting the exhaust gas stream and an outlet for passage of a treated exhaust stream having a reduced CO2 content, the treatment zone preferably operating in swing mode with at least two subsystems, each including a heat exchanger with an inlet for receiving the hot exhaust gas stream from the ICE for passage in heat exchange relation with the capture agent to release CO2 and regenerate the capture agent, and an outlet for the cooled exhaust gas stream, the treatment zone having a CO2 discharge outlet for CO2 released from the regenerated capture agent; b. a compression zone in fluid communication with the CO2 discharge outlet from the treatment zone, the compression zone including one or more compressors for reducing the volume of the CO2; c. a storage zone for receiving the compressed CO2 for temporary storage on board the vehicle; and d. an exhaust gas conduit in fluid communication with the treated exhaust gas stream outlet from the treatment zone.