  Consider the Hamiltonian action of a compact connected Lie group on a
transversely symplectic foliation which satisfies the transverse hard Lefschetz
property. We establish an equivariant formality theorem and an equivariant
symplectic $d\delta$-lemma in this setting. As an application, we show that if
the foliation is also Riemannian, then there exists a natural formal Frobenius
manifold structure on the equivariant basic cohomology of the foliation.
