  Liouville domains are a special type of symplectic manifolds with boundary
(they have an everywhere defined Liouville flow, pointing outwards along the
boundary). Symplectic cohomology for Liouville domains was introduced by
Cieliebak-Floer-Hofer-Wysocki and Vitero. The latter constructed a restriction
(or transfer) map associated to an embedding of one Liouville domain into
another.
  In this preprint, we look at exact Lagrangian submanifolds with Legendrian
boundary inside a Liouville domain. The analogue of symplectic cohomology for
such submanifolds is called "wrapped Floer cohomology". We construct an
A_\infty-structure on the underlying wrapped Floer complex, and (under suitable
assumptions) an A_\infty-homomorphism realizing the restriction to a Liouville
subdomain. The construction of the A_\infty-structure relies on an
implementation of homotopy direct limits, and involves some new moduli spaces
which are solutions of generalized continuation map equations.
