What is the proper pronunciation for an Ashkenazi Jew living in Israel? I recently heard that Rav Kook supported maintaining the traditional Ashkenazi pronunciation, although it appears as if only the Haredi world maintains this pronunciation.

Ashkenazi Jews who grew up with European Ahshkenazi pronunciation and feel comfortable praying and learning with this pronunciation should continue to do so and certainly can teach this pronunciation to their children. Those who feel more comfortable with mordern Israeli pronunciation may change. Since it is permissable to pray in any language, even if one of the pronuciations is incorrect, this does not prevent proper prayer. There are followers of Rav Kook who use modern pronunciation, but say the name of Hashem as A-do-noi (the European Ashkenazi way) instead of A-do-nai (the modern Israeli way). The more common opinion (outside of Ashkenazi Haredi custom) is that one may use the pronunciation with which one is most at home.