  We prove higher regularity for nonlinear nonlocal equations with possibly
discontinuous coefficients of VMO-type in fractional Sobolev spaces. While for
corresponding local elliptic equations with VMO coefficients it is only
possible to obtain higher integrability, in our nonlocal setting we are able to
also prove a substantial amount of higher differentiability, so that our result
is in some sense of purely nonlocal type. By embedding, we also obtain higher
H\"older regularity for such nonlocal equations.
