On the index theorem for symplectic orbifolds. (Q1774074)

The authors deal with deformation quantization on a symplectic orbifold. The methods of Kawasaki and Vergne for the index theorem for elliptic operators on orbifolds as well as Fedosov's methods for the index theorem for the deformation quantization of a symplectic manifold are well known. In this paper, the authors try to combine these methods in order to generalize the index theorem in the orbifold case. Actually, this paper gives an explicit construction of the trace, but the index formula is only a conjecture. A brief description of the Picard group is also given, and many facts which support and motivate the index formula conjecture are discussed.