Cobordism-framed correspondences and the Milnor $ K$-theory

The 0th cohomology group is computed for a complex of groups of cobordism-framed correspondences. In the case of ordinary framed correspondences, an analogous computation was completed by A. Neshitov in his paper "Framed correspondences and the Milnor-Witt $ K$-theory". Neshitov's result is, at the same time, a computation of the homotopy groups $ \pi _{i,i}(S^0)(\mathop {Spec}(k))$, and the present work might be used subsequently as a basis for computing the homotopy groups $ \pi _{i,i}(MGL_{\bullet })(\mathop {Spec}(k))$ of the spectrum $ MGL_{\bullet }$.