Infinitesimal Generators of C *-Algebras

We develop the method introduced previously, to construct infinitesimal generators on locally compact group C^*-algebras and on tensor product of C^*-algebras. It is shown in particular that there is a C^* -algebra A such that the C^*-tensor product of A and an arbitrary C^*-algebra B can have a non-approximately inner strongly one parameter group of ^*-automorphisms.