A C*-algebra is said be Z-absorbing if it absorbs the Jiang-Su algebra Z tensorially. Let us consider a free and minimal Z^d action, and let us consider the corresponding crossed product C*-algebra. Then it is shown recently that the Z-absorption of the crossed product C*-algebra, which is a C*-algebra property, indeed is completely characterized by the small boundary property (or the zero mean dimension) of the canonical Cartan subalgebra, which is a dynamical system property or a Cartan subalgebra property. As a consequence, the Z-absorption of the crossed product C*-algebra can be also characterized by other (C*-algebra or Cantan subalgebra) properties such as uniform property Gamma or real rank of certain sequence algebras. The talk is base on joint works with George A. Elliott.