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Given a monotone Lagrangian submanifold invariant under a loop of Hamiltoniandiffeomorphisms, we compute a piece of the closed-open string map into theHochschild cohomology of the Lagrangian which captures the homology class ofthe loop's orbit.  Our applications include split-generation and non-formality results for realLagrangians in projective spaces and other toric varieties; a particularlybasic example is that the equatorial circle on the 2-sphere carries anon-formal Fukaya A-infinity algebra in characteristic two.

The closed-open string map for $S^1$-invariant Lagrangians