  We consider a Dirac-type operator $D_P$ on a vector bundle $V$ over a compact
Riemannian manifold $(M,g)$ with a nonempty boundary. The operator $D_P$ is
specified by a boundary condition $P(u|_{\p M})=0$ where $P$ is a projector
which may be a non-local, i.e. a pseudodifferential operator. We assume the
existence of a chirality operator which decomposes $L^2(M, V)$ into two
orthogonal subspaces $X_+ \oplus X_-$. Under certain conditions, the operator
$D_P$ restricted to $X_+$ and $ X_-$ defines a pair of Fredholm operators which
maps $X_+\to X_-$ and $X_-\to X_+$ correspondingly, giving rise to a
superstructure on $V$. In this paper we consider the questions of determining
the index of $D_P$ and the reconstruction of $(M, g), V$ and $D_P$ from the
boundary data on $\p M$. The data used is either the Cauchy data, i.e. the
restrictions to $\p M \times \R_+$ of the solutions to the hyperbolic Dirac
equation, or the boundary spectral data, i.e. the set of the eigenvalues and
the boundary values of the eigenfunctions of $D_P$. We obtain formulae for the
index and prove uniqueness results for the inverse boundary value problems. We
apply the obtained results to the classical Dirac-type operator in $M\times
\C^4$, $M \subset \R^3$.
