  Consider the wrapped Fukaya category W of a collection of exact Lagrangians
in a Liouville manifold. Under a non-degeneracy condition implying the
existence of enough Lagrangians, we show that natural geometric maps from the
Hochschild homology of W to symplectic cohomology and from symplectic
cohomology to the Hochschild cohomology of W are isomorphisms, in a manner
compatible with ring and module structures. This is a consequence of a more
general duality for the wrapped Fukaya category, which should be thought of as
a non-compact version of a Calabi-Yau structure. The new ingredients are: (1)
Fourier-Mukai theory for W via a wrapped version of holomorphic quilts, (2) new
geometric operations, coming from discs with two negative punctures and
arbitrary many positive punctures, (3) a generalization of the Cardy condition,
and (4) the use of homotopy units and A-infinity shuffle products to relate
non-degeneracy to a resolution of the diagonal.
