  We investigate general elliptic boundary-value problems in H\"ormander inner
product spaces that form the extended Sobolev scale. The latter consists of all
Hilbert spaces that are interpolation spaces with respect to the Sobolev
Hilbert scale. We prove that the operator corresponding to an arbitrary
elliptic problem is Fredholm in appropriate couples of the H\"ormander spaces
and induces a collection of isomorphisms on the extended Sobolev scale. We
obtain a local a priory estimate for generalized solutions to this problem and
prove a theorem on their local regularity in the H\"ormander spaces. We find
new sufficient conditions under which generalized derivatives (of a given
order) of the solutions are continuous.
