  We study the production of a mixed scalar-pseudoscalar Higgs boson in gluon
fusion at the LHC, through next-to-next-to-leading order (NNLO) in QCD. We
obtain fully differential results, including the decay of the Higgs boson to
two charged lepton pairs. We discuss the impact of the interference between the
scalar and pseudoscalar states. We also show differential distributions for
several kinematic variables whose shape is sensitive to the parity of the Higgs
boson, and assess the impact of the NNLO QCD corrections on these shapes.
