A support body is described which has an adsorber material for adsorbing nitrogen oxides in an exhaust gas which is generated in at least one combustion chamber of an internal-combustion engine. A method is described for operating an internal-combustion engine having an exhaust system which has a support body of this type. All the combustion chambers of the internal-combustion engine together have an overall combustion chamber volume, and the support body has an adsorber volume. The adsorber volume is configured to be less than 75%, in particular less than 45%, and preferably even less than 5% of the combustion-chamber volume. A support body of this type ensures a good cold-starting performance of the exhaust system and prevents the emission of nitrogen oxides, in particular when using the proposed method of operating the exhaust system.