An apparatus for supplying breathing air to a person includes a rebreathing system arranged in the air supply circuit, which removes CO2 at least in part present in the person's expiration air with a CO2 absorber, and treats the expiration air to supply treated air to the person again as inhalation air. The apparatus includes a condensate collection container (9) collecting water forming in the air supply circuit. The condensate collection container (9) is arranged at least in part below a reaction zone (17) of the CO2 absorber (1). At least one heat exchanger (10, 14) is provided in the CO2 absorber, via which heat from the air, which flows through the CO2 absorber and is heated as a result of the exothermic CO2 absorption reaction occurring in the reaction zone of the CO2 absorber, is dissipated.