(Z2)k-actions and the minimal data of the normal bundle

Let denote the group of the n-dimensional unoriented cobordism classes containing a representative that admits a (Z2)k-action with the fixed point set of constant dimension n−r and . In this paper, we introduce the minimal data of the normal bundle which reflects the complexity of the (Z2)k-action. Such minimal data or their upper bounds are determined for some r and k.