Tom Dieck introduced a commutative triangle whereby the exponential morphism from the Burnside functor to the unit functor is factorized through the real representation functor. Tornehave introduced a p-adic variant of the exponential morphism. His construction involves real representations that are not well defined up to isomorphism. To obtain a well defined commutative triangle, we introduce the orientation functor, a quotient of the real representation functor. © Taylor & Francis Group, LLC.