Coronas and Callias type operators in coarse geometry

We interpret the coarse symbol and index class of a Callias type Dirac operator $D+\mathrm{\Psi }$ on a manifold $M$ as a pairing between the coarse symbol and index classes associated to $D$ and K-theory classes of the coarse corona of $M$ or $M$ itself determined by $\mathrm{\Psi }$. Local positivity of $D$ and local invertibility of $\mathrm{\Psi }$ are incorporated in terms of support conditions on the $K$-theoretic level.