  Given a subgroup H of a finite group G, we begin a systematic study of the
partial representations of G that restrict to global representations of H.
After adapting several results from [DEP00] (which correspond to the case where
H is trivial), we develop further an effective theory that allows explicit
computations. As a case study, we apply our theory to the symmetric group and
its subgroup of permutations fixing 1: this provides a natural extension of the
classical representation theory of the symmetric group.
