  We study the low-temperature thermodynamics of a spin-S magnetic impurity
coupled to m degenerate bands of interacting electrons in one dimension. By
exploiting boundary conformal field theory techniques, we derive exact results
for the possible impurity thermal and magnetic response. The leading behavior
of the impurity magnetic susceptibility is shown to be insensitive to the
electron-electron interaction. In contrast, there are two types of scaling
behavior of the impurity specific heat consistent with the symmetries of the
problem: Either it remains the same as for the ordinary multichannel Kondo
problem for noninteracting electrons, or it acquires a new leading term
governed by an interaction-dependent critical exponent. We conjecture that the
latter behavior is indeed realized when the impurity is exactly screened
(m=2S).
