  Let G be a split connected reductive group over a local non-archimedean
field. We classify all irreducible complex G-representations in the principal
series, irrespective of the (dis)connectedness of the centre of G. This leads
to a local Langlands correspondence for principal series representations, which
satisfies all expected properties. We also prove that the ABPS conjecture about
the geometric structure of Bernstein components is valid throughout the
principal series of G.
