the $\star$-product of two chiral fields will not be a chiral field. Therefore we have to use the method of projectors to decompose the $\star$-products of fields into their irreducible components. Collecting the terms invariant under the twisted SUSY transformations we construct the deformed Wess-Zumino action.

Being interested in implications of the twisted symmetry on renormalizability properties, in this paper we calculate the divergent part of the one-loop effective action. More precisely, we calculate divergent parts of the one-point and the two-point functions. The plan of the paper is as follows: In the next section we summarize the most important properties of our model, more details of the construction are given in [@miSUSY]. In Section 3 we describe the method we use to calculate divergent parts of the $n$-point Green functions: the background field method and the supergraph technique. In Sections 4 the tadpole diagram and the divergent part of the two-point function are calculated. Finally, we discuss renormalizability of the model. We give some comments and compare our results with the results already present in the literature. Some details of our calculations are presented in the Appendix.

Construction of the model
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There are different ways to realize a 