Chern-Simons terms on noncommutative branes

We write down couplings of the fields on a single BPS Dp-brane with noncommutative world-volume coordinates to the RR-forms in type-II theories, in a manifestly background independent way. This generalises the usual Chern-Simons action for a commutative Dp-brane. We show that the noncommutative Chern-Simons terms can be mapped to Myers terms on a collection of infinitely many D-instantons. We also propose Chern-Simons couplings for unstable non-BPS branes, and show that condensation of noncommutative tachyons on these branes leads to the correct Myers terms on the decay products.