  Let F be a non-archimedean local field of odd residual characteristic p. Let
G be a (connected) reductive group that splits over a tamely ramified field
extension of F. We show that a construction analogous to Yu's construction of
complex supercuspidal representations yields smooth, irreducible, cuspidal
representations over an arbitrary algebraically closed field R of
characteristic different from p. Moreover, we prove that this construction
provides all smooth, irreducible, cuspidal R-representations if p does not
divide the order of the Weyl group of G.
