  We develop an obstruction theory for the existence and uniqueness of a
solution to the gluing problem for a destriction functor and apply it to some
well-known biset functors. The obstruction groups for this theory are reduced
cohomology groups of a category ${\mathcal D}_G$, whose objects are the
sections $(U,V)$ of $G$ with $V\neq 1$, and whose morphisms are defined as a
generalization of morphisms in the orbit category. Using this obstruction
theory, we calculate the obstruction group for the Dade group of a $p$-group
when $p$ is odd.
