Crossed Burnside rings and Boucʹs construction of Green functors

We use a formula for primitive idempotents of the crossed Burnside ring given by F. Oda and T. Yoshida, and a result from the theory of Green functors obtained by S. Bouc to prove an induction theorem for the Drinfelʹd double for a finite group over the complex field. We obtain Artinʹs induction theorem for group algebras as a corollary of the theorem.