Given a symplectic cohomology class of degree 1, we define the notion of an
equivariant Lagrangian submanifold. The Floer cohomology of equivariant
Lagrangian submanifolds has a natural endomorphism, which induces a grading by
generalized eigenspaces. Taking Euler characteristics with respect to the
induced grading yields a deformation of the intersection number. Dehn twists
act naturally on equivariant Lagrangians. Cotangent bundles and Lefschetz
fibrations give fully computable examples. A key step in computations is to
impose the "dilation" condition stipulating that the BV operator applied to the
symplectic cohomology class gives the identity. Equivariant Lagrangians mirror
equivariant objects of the derived category of coherent sheaves.Comment: 32 pages, 9 figures, expanded introduction, added details of example
7.5, added discussion of sign
