The present invention relates to an apparatus for decarbonization of calcium carbonate into carbon dioxide rich exhaust gas comprising: a reactor 30 for releasing the CO2 by decarbonization of CaCO3; a duct 33 for forwarding the CO2 rich exhaust gas generated in the reactor for further processing; a system for recirculation of at least a portion of the CO2 rich exhaust gas generated in the reactor back into the reactor; a firing system 10 for indirect heating of the reactor; and means for indirect heating 11. Also a system for capturing CO2 from an exhaust gas comprising a first reactor 120 wherein the carbon dioxide present in the flue gas is captured from the flue gases by carbonization; a second reactor 130 to which the solid material contained in the flue gases output from the first reactor are transferred, wherein the said solid material are subject for heat treatment in order to extract carbon dioxide therefrom by decarbonization; means 111 for indirect heating of the second reactor 130; means 150 for transferring the exhaust gas generated by the means for indirect heating of the second reactor, to the first reactor; means 133 for transporting the captured carbon dioxide for further processing.