Electronic Journal of Differential Equations, Conference 04 (2000), pp. 23-35. Title: Extension techniques in C*-cross Products by compact group duals and in quantum field theory Authors: Roberto Conti (Univ.  di Roma "Tor Vergata", Italy) Claudio D'Antoni (Univ.  di Roma "Tor Vergata", Italy) Abstract: Using the methods developed in a previous paper, we consider the problem of extending endomorphisms to cross-product by compact group duals. Then we discuss some other applications to quantum field theory, mainly in connection with PCT symmetries. Published July 12, 2000. Math Subject Classifications: 81T05, 46L60. Key Words: C*-crossed products; quantum field theory.