Equivariant forms of connective K-theory (Q1296314)

This paper gives a construction of a \(G\)-spectrum \({\mathbb E}\) representing a form of \(G\)-equivariant connective \(K\)-theory for \(G\) a group of order \(p\). The spectrum \({\mathbb E}\), which is constructed using the Tate pull-back square developed by the author and \textit{J. P. May} in [Generalized Tate cohomology, Mem. Am. Math. Soc. 543 (1995; Zbl 0876.55003)], has the properties: (1) \(\mathbb E\) is split ring spectrum, non-equivariantly \(ku\), (2) \({\mathbb E} [v^{-1}] \cong K\) (equivariantly), (3) \(\mathbb E\) is complex orientable (equivariantly), (4) \({\mathbb E}^*_G\) is a Noetherian ring, and (5) \({\mathbb E}^G_*\) is concentrated in even degrees. The author also shows that other known candidates for such a spectrum \(\mathbb E\) do not have all five of these properties.