We consider fractional Sobolev spaces H-theta(Gamma), theta is an element of[0, 1] on a 2D surface Gamma. We show that functions in H-theta(Gamma) can be decomposed into contributions with local support in a stable way. Stability of the decomposition is inherited by piecewise polynomial subspaces. Applications include the analysis of additive Schwarz preconditioners for discretizations of the hypersingular integral operator by the p-version of the boundary element method with condition number bounds that are uniform in the polynomial degree p.