10 of the carrier matrix shell 2 are connected to one another in such a way that they can expand to different extents in particular in axial direction this firstly requires the metal foils 4 5 to be connected at their ends 11 12 only at the innermost layer 8 of the carrier matrix shell 2 in at least one connecting section 15 which preferably lies adjacent a fluid inlet side end 13 of the honeycomb body 1 as is illustrated in fig4 0044 fig4 also shows that in particular in order to avoid a telescopic action on the part of the carrier matrix 3 the ends 11 12 of the metal foils 4 5 are additionally connected to the innermost layer 8 in a connecting section 16 which is adjacent a fluid outlet side end 14 of the honeycomb body 1 if the honeycomb body 1 has only a short axial length l of for example only l 25 mm or l 35 mm in a non illustrated embodiment the ends 11 12 of the metal foils 4 5 may also be connected to the innermost layer 8 of the carrier matrix shell 2 over their entire axial length l the layers 8 9 10 of the carrier matrix shell 2 are preferably connected to one another predominantly through the use of a joining technique in particular by welding brazing or adhesive bonding 0046 fig4 also shows that the innermost layer 8 of the carrier matrix shell 2 is connected to the next outer layer which in the exemplary embodiment is in fact the outermost layer 10 of the carrier matrix shell 2 the connection is provided in a connecting section 17 which is disposed symmetrically with respect to a longitudinal axis 6 of.