We complete the study of the Gysin morphism started in a previous prepublication (cf K-theory preprint archive 0690). This allows to define the Gysin morphism associated to a projective morphism and prove other formulas which for example explain its relation with residue morphisms. The general construction allows to construct a canonical isomorphism of the Cousin complex and the Gersten complex for a suitable cohomology theory. This preprint is identical to the preprint no. 2005-30 put on the server of the LAGA (Paris 13) on June 30, 2005.