  We consider a chirally invariant lattice Higgs-Yukawa model based on the
Neuberger overlap operator. As a first step towards the eventual determination
of Higgs mass bounds we present the phase structure of the model analytically
in the large Nf-limit in the physically interesting region of the Yukawa
coupling constant. We confront the analytically obtained phase diagram with
corresponding HMC-simulations and find an excellent agreement at large values
of Nf. In the opposite case the large Nf computation still gives a good
qualitative description of the phase diagram. We also present first and very
preliminary results on the Higgs upper bound at one selected cut-off of the
theory.
