Regular Bernstein blocks

Abstract For a connected reductive group G defined over non-archimedean local field F , we consider the Bernstein blocks in category of smooth representations G ⁢ ( F stretchy="false">) {G(F)} . whose cuspidal support involves regular supercuspidal representation are called blocks. Most when residual characteristic is not too small. Under mild hypotheses on characteristic, show that center block isomorphic to depth-zero 0 {G^{0}(F)} where {G^{0}} certain twisted Levi subgroup In some cases, themselves equivalent, and as consequence prove ABPS Conjecture new cases.