  We consider an arbitrary linear elliptic first--order differential operator A
with smooth coefficients acting between sections of complex vector bundles E,F
over a compact smooth manifold M with smooth boundary N. We describe the
analytic and topological properties of A in a collar neighborhood U of N and
analyze various ways of writing A|U in product form. We discuss the sectorial
projections of the corresponding tangential operator, construct various
invertible doubles of A by suitable local boundary conditions, obtain Poisson
type operators with different mapping properties, and provide a canonical
construction of the Calderon projection. We apply our construction to
generalize the Cobordism Theorem and to determine sufficient conditions for
continuous variation of the Calderon projection and of well--posed selfadjoint
Fredholm extensions under continuous variation of the data.
