For the catalytic reaction of exhaust gases in an exhaust system, in particular an exhaust system for use in internal combustion engines, a device is proposed with a catalyst carrier element (1) which is provided with a plurality of channels (2) through which the exhaust gas can flow. The free cross section (4) of flow of the channels (2) is partially closed in the direction of flow of the exhaust gas by plastic deformation of the channel walls (11), specifically, in an outer ring region (3) of the catalyst carrier element (1). The plastic deformation can be carried out using, for example, a tool (17) provided for this purpose with a disc (18) which can rotate about an axis (19). The disc (18) is forced against the catalyst carrier element (1) and the casing (10) to create a plastic deformation of the casing tube (10) and channel walls (11) in the form of a peripheral crimp (20) pointing towards the carrier element (1). Other techniques can be applied to create the plastic deformation. The outer channels thus closed off form a thermal insulation against the casing tube (10) which helps the catalyst carrier element (1) to heat up more rapidly in the cold start phase.