Abstract: Let J^r_n,k denote the set of ndimensional cobordism class containing a representative Mⁿ admitting a (Z₂)^kaction with fixed point set of constant codimension r. J^r_*,k is an idea of the unoriented cobordism ring MO_*. In this paper, special generators of MO_* are constructed to prove that consists of all classes of dimension greater than 2^k+2^l and the decomposables of dimension 2^k+2^l in which each factor of monomials has dimension less than 2^k.

Key words: (Z₂)^kaction, cobordism class, fixed point set, projective space bundle