Abstract. Let F be a non-archimedean local field of residual characteristic different from 2, and let G be a unitary, symplectic or orthogonal group, considered as the fixed point subgroup in = GL(N,F) of an involution σ. We generalize the notion of a simple character for , which was introduced by Bushnell and Kutzko [Annals of Mathematics Studies 129 (Princeton University Press, 1993)], to define semisimple characters. Given a semisimple character θ for fixed by σ, we transfer it to a character θ_- for G and calculate its intertwining. If the torus associated to θ_- is maximal compact, we obtain supercuspidal representations of G, which are new if the torus is split only over a wildly ramified extension.