Coşkun O.Yalçin, E.2016-02-082016-02-0820090022-4049http://hdl.handle.net/11693/22701We generalize the fundamental theorem for Burnside rings to the mark morphism of plus constructions defined by Boltje. The main observation is the following: If D is a restriction functor for a finite group G, then the mark morphism φ : D+ → D+ is the same as the norm map of the Tate cohomology sequence (over conjugation algebra for G) after composing with a suitable isomorphism of D+. As a consequence, we obtain an exact sequence of Mackey functors 0 → over(Ext, ̂)γ - 1 (ρ, D) → D+ over({long rightwards arrow}, φ) D+ → over(Ext, ̂)γ 0 (ρ, D) → 0 where ρ denotes the restriction algebra and γ denotes the conjugation algebra for G. Then, we show how one can calculate these Tate groups explicitly using group cohomology and give some applications to integrality conditions. © 2008 Elsevier B.V. All rights reserved.EnglishArticle10.1016/j.jpaa.2008.11.025