Cobordism of G-manifolds

We survey some results in the field of equivariant cobordism. In particular, we use methods from equivariant stable homotopy theory to calculate the unoriented $C_2$-equivariant bordism ring ${\mathrm{\Omega }}_{\ast }^{C_2}$, which was originally calculated by Alexander using other methods. Our proof method generalizes well to other settings, such as equivariant complex cobordism, and affords a formal group theoretic interpretation of Alexander’s calculation.