Classification up to cobordism of manifolds with simple action of $\mathbb Z/p$

We deal with quasi-complex manifolds with an action of the group $\mathbb Z/p$ such that the set of fixed points of this action has a trivial normal bundle. The set of cobordism classes of these manifolds is described in terms of the coefficients of the formal group of geometric cobordisms and in terms of characteristic numbers. We also establish the relationship between this work and relevant papers containing a solution of this problem in some particular cases.