Abstract
We develop an obstruction theory for the existence and uniqueness of a solution to the gluing problem for a biset functor defined on the subquotients of a finite group G. The obstruction groups for this theory are the reduced cohomology groups of a category DG⁎ whose objects are the sections (U,V) of G, where 1≠V⊴U≤G, and whose morphisms are defined as a generalization of morphisms in the orbit category. Using this obstruction theory, we calculate the obstruction group for some well-known p-biset functors, such as the Dade group functor defined on p-groups with p odd.
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