deformation of the classical action (\[SGaction\]) is only present in the interaction term, and terms in the action quadratic in the deformation parameter will always be of the third order in fields. We have to conclude that our model, as it stands, is not renormalizable.

Discussion and conclusions
==========================

Let us now summarize what we have done so far and discuss the obtained results in more detail.

In order to see how different deformations (different twists) affect renormalizability of the Wess-Zumino model, we considered one special example of twist, (\[twist\]). The main adventage of this twist is that it is hermitian and therefore implies the hermitian $\star$-product. Compared with the undeformed SUSY Hopf algebra, the twisted SUSY Hopf algebra changes. In particular, the Leibniz rule (\[deftrlaw\]) becomes deformed. The notion of chirality is lost and we had to apply the method of projectors introduced in [@miSUSY] to obtain the action. A nonlocal deformation of the commutative Wess-Zumino action invariant under the deformed SUSY transformations (\[defsusytr\]) and with a good commutative limit was introduced and its renormalizability properties were investigated. Notice that the nonlocality comes from the application of the chiral projector $P_2$[^1].

To calculate the divergent part of the effective 