  We prove Hoelder continuity for n/2-harmonic maps from subsets of Rn into a
sphere. This extends a recent one-dimensional result by F. Da Lio and T.
Riviere to arbitrary dimensions. The proof relies on compensation effects which
we quantify adapting an approach for Wente's inequality by L. Tartar, instead
of Besov-space arguments which were used in the one-dimensional case. Moreover,
fractional analogues of Hodge decomposition and higher order Poincare
inequalities as well as several localization effects for nonlocal operators
similar to the fractional laplacian are developed and applied.
