Moduli of Bundles on Exotic Del Pezzo Orders

We study bundles on rank 4 maximal orders on P ramified on a smooth plane quartic. We compute the possible Chern classes for line bundles. Our main result is that the moduli space of line bundles with minimal second Chern class is either a point or a smooth genus two curve. Throughout, all objects and maps are assumed to be defined over some algebraically closed base field k of characteristic 0. Modules will by default be left modules unless otherwise noted.