  We prove a Tannaka duality theorem for $(\infty,1)$-categories. This is a
duality between certain derived group stacks, or more generally certain derived
gerbes, and symmetric monoidal $(\infty,1)$-categories endowed with particular
structure. This duality theorem is defined over commutative ring spectra and
subsumes the classical statement. We show how the classical theory, and its
extension over arbitrary rings, arises as a special case of our more general
theory. The application to perfect complexes is explored.
