  We give a general formula for the defect appearing in the Verdier-type
Riemann-Roch formula for Chern-Schwartz-MacPherson classes in the case of a
regular embedding. Our proof of this formula uses the constructible function
version of Verdier's specialization functor, together with a specialization
property of Chern-Schwartz-MacPherson classes and the corresponding
Riemann-Roch theorem for smooth morphisms. As a very special case we get a
formula for the Milnor-class of a local complete intersection in a smooth
manifold, which in the case of a hypersurface gives back a result of
Parusinski-Pragacz.
