Criminal law in multicultural societies: the crimes committed for a "cultural motivation" by immigrants

Due to the last decades' massive migratory flows, many people and families coming from abroad now live in Italy and in other European countries. These persons find that in the immigration nation rules of conduct - and in particular criminal norms - are in force which are different from those in force in their native countries; and in some cases such differences are grounded on deeper cultural differences. As a result, some conducts, while being tolerated by the immigrants' native culture, are deemed criminal by the immigration country. How should criminal law deal with those cases in which an immigrant commits a culturally motivated crime? Should it recognize him or her some ( partial or complete) cultural defense? And, if yes, in what way should this recognition occur? By the enactment of new specific norms, or by a culturally sensitive interpretation of existing norms?