Logarithmic trace and orbifold products

Abstract

We give a purely equivariant construction of orbifold products for quotient Deligne-Mumford stacks [X/G] where G is an arbitrary linear algebraic group (not necessarily finite). The key to our construction is the definition of the "logarithmic trace" of an equivariant vector bundle. We also prove that there is an orbifold Chern character homomorphism which induces an isomorphism of a canonical summand in the orbifold Grothendieck ring with the orbifold Chow ring. As an application we obtain an associative orbifold product on the Grothendieck ring of [X/G] (as opposed to its inerita stack) taken with complex coefficients.

39 pages, references and a few remarks added

References in corpus (1)

• The Drinfel'd Double and Twisting in Stringy Orbifold Theory

Cited by in corpus (11)

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• Strong regular embeddings of Deligne-Mumford stacks and hypertoric geometry
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• The Moduli Space in the Gauged Linear Sigma Model
• Motivic multiplicative McKay correspondence for surfaces
• Equivariant commutative stringy cohomology rings on almost complex manifolds
• Equivariant cohomology for Hamiltonian torus actions on symplectic orbifolds
• Inertial Chow rings of toric stacks
• Delocalized Chern character for stringy orbifold K-theory