On graded semigroup \(C^*\)-algebras and Hilbert modules (Q2041548)

Let \(S\) be a cancellative semigroup with identity \(e\), \(C^*_r(S)\) its reduced semigroup, \(G\) a group, and let \(\sigma:S\to G\) be a surjective semigroup homomorphism. Then a natural topological \(G\)-grading \(\{\mathfrak A_g:g\in G\}\) is constructed on \(C^*_r(S)\). If \(G\) is finite, then a projective Hilbert \(C^*\)-module structure (over \(\mathfrak A_e\)) is introduced on \(C^*_r(S)\).