Kramer's Degeneracy and Antiferromagnetism

How can one understand the concept of Kramer's Degeneracy for an antiferromagnetic system where spin-up and spin-down bands overlap due to net zero magnetic moment?

You may want to have a look at my answer to a related question. Basically, in the usual single-particle-model picture of an antiferromagnetic system, the total wavefunction is like $$\Psi=|\uparrow\downarrow\uparrow\downarrow\uparrow\downarrow\cdots\rangle$$. Its time-reversed version, $$\tilde{\Psi}=|\downarrow\uparrow\downarrow\uparrow\downarrow\uparrow\cdots\rangle$$, amounts to the system where every spin of the antiferromagnetic system is flipped, which certainly has the same energy as $$\Psi$$. Therefore the Kramers degeneracy is present, but only on a global level.