Let G be a finite solvable group. If F is a saturated formation, the F-projectors of G are defined as the unique G-conjugacy class of subgroups H such that HN/N is a maximal F-subgroup of G for every normal subgroup N of G. In 2022, G. Navarro introduced a canonical subset Irr_F'(G) of the irreducible characters of G, in bijection with the irreducible characters of N_G(H)/H', where H is an F-projector of G. In this talk, I will discuss several aspects of Irr_F'(G), from the construction of the subset to the behaviour of these characters with respect to restriction to certain subgroups. The case where F is the formation of nilpotent groups will be of particular interest.