  For three classes of elliptic pseudodifferential operators on a compact
manifold with boundary which have `geometric K-theory', namely the
`transmission algebra' introduced by Boutet de Monvel, the `zero algebra'
introduced by Mazzeo and the `scattering algebra' from [MR95k:58168] we give
explicit formulae for the Chern character of the index bundle in terms of the
symbols (including normal operators at the boundary) of a Fredholm family of
fibre operators. This involves appropriate descriptions, in each case, of the
cohomology with compact supports in the interior of the total space of a vector
bundle over a manifold with boundary in which the Chern character, mapping from
the corresponding realization of K-theory, naturally takes values.
