Dirac and Laplace operators on some non-orientable conformally flat orbifolds

In this paper we present an explicit construction of the fundamental solution to the Dirac and Laplace operator on some non-orientable conformally flat manifolds and special orbifolds. We first treat a class of projective cylinders and tori where we can study monogenic sections with values in different pin bundles. Then we discuss the Möbius strip, the Klein bottle and higher dimensional generalizations of them. We present integral representation formulas together with some elementary tools of harmonic analysis on these manifolds resp. orbifolds.