Construction of tame supercuspidal representations in arbitrary residue characteristic

Let F be a nonarchimedean local field whose residue field has at least four elements. Let G be a connected reductive group over F that splits over a tamely ramified field extension of F. We provide a construction of supercuspidal representations of G(F) via compact induction that contains, among others, all the supercuspidal representations constructed by Yu in 2001, but that also works in residual characteristic two. The input for our construction is described uniformly for all residual characteristics and is analogous to Yu's input except that we do not require our input to satisfy the second genericity condition (GE2) that Yu imposes.