Graded C∗-algebras

C∗-algebras graded by a semilattice appeared for the first time in the study of the quantum N body problem. We show that these algebras are completely described by their homogeneous subalgebras and that they are invariant under several operations of C∗-algebras such as tensor products. We give the K-theory of graded C∗-algebras and we study some of their properties from the C∗-algebra point of view.