  In a class of inner product H\"ormander spaces, we investigate a general
elliptic problem for which the maximum of orders of boundary conditions is
grater than or equal to the order of elliptic equation. The order of regularity
for these spaces is an arbitrary radial positive function RO-varying at
infinity in the sense of Avakumovi\'c. We prove that the operator of the
problem under investigation is bounded and Fredholm on appropriate pairs of
H\"ormander spaces indicated. A theorem on isomorphism generated by this
operator is proved. For generalized solutions to this problem, we establish a
local a priory estimate and prove a theorem about their local regularity in
H\"ormander spaces. As application, we obtain new sufficient conditions under
which given derivatives of the solutions are continuous.
