  I conjecture that index formulas for $K$-theory classes on the moduli of
holomorphic $G$-bundles over a compact Riemann surface $\Sigma$ are controlled,
in a precise way, by Frobenius algebra deformations of the Verlinde algebra of
$G$. The Frobenius algebras in question are twisted $K$-theories of $G$,
equivariant under the conjugation action, and the controlling device is the
equivariant Gysin map along the "product of commutators" from $G^{2g}$ to $G$.
The conjecture is compatible with naive virtual localization of holomorphic
bundles, from $G$ to its maximal torus; this follows by localization in twisted
$K$-theory.
