Abstract: The automorphism group of a C*-algebra can be enriched to a crossed module taking into account that inner automorphisms are more trivial than general automorphisms. I give some examples how crossed modules act on C*-algebras and then examine the case of Abelian crossed modules. I generalise Takesaki-Takai duality to a duality between actions of an Abelian crossed module an actions of a groupoid. If time permits, I show how to decompose any crossed module of Lie groups into an extension of an ordinary Lie group by Abelian crossed modules.