  We provide an equivariant extension of the bivariant Cuntz semigroup
introduced in previous work for the case of compact group actions over
C*-algebras. Its functoriality properties are explored and some well-known
classification results are retrieved. Connections with crossed products are
investigated, and a concrete presentation of equivariant Cuntz homology is
provided. The theory that is here developed can be used to define the
equivariant Cuntz semigroup. We show that the object thus obtained coincides
with the recently proposed one by Gardella and Santiago, and we complement
their work by providing an open projection picture of it.

Operator Algebras;Functional Analysis