  First we describe a class of homotopy Frobenius algebras via cyclic operads
which we call cyclic $A_\infty$ algebras. We then define a suitable new
combinatorial operad which acts on the Hochschild cochains of such an algebra
in a manner which encodes the homotopy BV structure. Moreover we show that this
operad is equivalent to the cellular chains of a certain topological
(quasi)-operad of CW complexes whose constituent spaces form a homotopy
associative version of the Cacti operad of Voronov. These cellular chains thus
constitute a chain model for the framed little disks operad, proving a cyclic
$A_\infty$ version of Deligne's conjecture. This chain model contains the
minimal operad of Kontsevich and Soibelman as a suboperad and restriction of
the action to this suboperad recovers their results in the unframed case.
Additionally this proof recovers the work of Kaufmann in the case of a strict
Frobenius algebra. We then extend our results to cyclic $A_\infty$ categories,
with an eye toward the homotopy BV structure present on the Hochschild cochains
of the Fukaya category of a suitable symplectic manifold.
