Equivariant connective K-theory for compact Lie groups

We construct a complex oriented, multiplicative, Noetherian, G-equivariant analogue of connective K-theory for an arbitrary compact Lie group G. Inverting the Bott element gives Atiyah–Segal equivariantK-theory and completion at the augmentation ideal gives non-equivariant connective K-theory of the Borel construction. We describe its role in the theory of equivariant formal group laws and calculate its coefficient ring for a variety of groups.