Title: Unoriented Spectral Triples,
Abstract: Any oriented Riemannian manifold with a Spin-structure defines a spectral
triple, so the spectral triple can be regarded as a noncommutative
Spin-manifold. Otherwise for any unoriented Riemannian manifold there is the
two-fold covering by oriented Riemannian manifold. Moreover there are
noncommutative generalizations of finite-fold coverings. This circumstances
yield a notion of unoriented spectral triple which is covered by oriented one.