Galois algebras and monoidal functors between categories of representations of finite groups

We use relations between Galois algebras and monoidal functors to describe monoidal functors between categories of representations of finite groups. W e pay special attention to two kinds of these monoidal functors: monoidal f unctors to vector spaces and monoidal equivalences between categories of re presentations. The functors of the second kind induce isomorphisms of chara cter tables. We show that pairs of groups with the same character table obt ained in this way are a generalization of the construction proposed by B. F ischer (1988, Rend. Circ. Mat. Palermo (2) Suppl. 19, 71-77). (C) 2001 Acad emic Press.