We prove a higher Atiyah-Patodi-Singer index theorem for Dirac operators twisted by C * -vector bundles. We use it to derive a general product formula for η-forms and to define and study new ρ-invariants generalizing Lott's higher ρ-form. The higher Atiyah-Patodi-Singer index theorem of Leichtnam-Piazza can be recovered by applying the theorem to Dirac operators twisted by the Mishenko-Fomenko bundle associated to the reduced C * -algebra of the fundamental group.