We develop a general Bethe ansatz formalism for diagonalizing an integ
rable model of a magnetic impurity of arbitrary spin coupled ferro- or
antiferromagnetically to a chain of interacting electrons. The method
is applied to an open chain, with the exact solution revealing the ex
istence of a ''hidden'' Kondo effect driven by forward electron scatte
ring off the impurity. We argue that the so-called ''operator reflecti
on matrices'' proposed in recent Bethe ansatz studies of related model
s emulate only forward electron-impurity scattering, which may explain
the absence of complete Kondo screening for certain values of the imp
urity-electron coupling in these models. [S0031-9007(98)07209-3].