the invention relates to a fully - metal heat exchanger comprising flat tubes , which have two narrow sides and two wide sides , and comprising fins which form a block together with the flat tubes , and comprising either at least one tube plate and one collecting tank , with edges of the collecting tank being connected , for example soldered , to edges of the tube plate , or at least one collecting tank which contains the tube plate , and having projections which are arranged at intervals . the invention leads to a heat exchanger which has a small installation space requirement while having comparatively good thermal properties in that , according to the invention , the projections engage in the ends of the flat tubes in the region of the narrow sides . the production method according to the invention accordingly provides that the projections are inserted into the ends of the flat tubes approximately in the region of the narrow sides .