superselection sectors, see [@AS] and references quoted therein. However, up until now, the localization properties of these sectors are not known, hence it is still not possible to investigate their charge structure.\
In the present paper we deal with the study of sectors of DHR-type in arbitrary globally hyperbolic spacetimes. Because of the sharp localization, sectors of DHR-type should be insensitive to the nontrivial topology of the spacetime, and their quantum numbers should exhibit the same features as in Minkowski space. However, the first investigations [@GLRV; @Rob3] have provided only partial results in this direction, and, in particular, they have pointed out that for particular classes of spacetimes the topology might affect the properties of sectors of DHR-type. The aim of the present paper is to show how this type of sectors and the topology of spacetime are related and that they manifest the properties described above also in an arbitrary globally hyperbolic spacetime. We want to stress that the results of this paper are confined to spacetimes whose dimension is $\geq 3$.\
Before entering the theory of DHR-sectors in globally hyperbolic spacetimes, a key fact has still to be mentioned. The DHR-analysis can be equivalently read in terms of 