J.P.C.Greenlees ``Equivariant forms of connective K-theory'' 18 pp A good equivariant version of connective complex K-theory is constructed for the group of prime order. This has the following properties (i) it is non-equivariantly ku, (ii) it is a split ring spectrum (iii) it becomes equivariant periodic K-theory if the Bott element is inverted (iv) it is complex orientable (v) its coefficient ring is Noetherian and in even degrees. (Added 19/11/97) [Comment (August 2000): A construction is now available for all compact Lie groups. It is known to have properties (i), (ii) and (iii) in general, and (iv) if the groupo is abelian. Its coefficient ring is Noetherian in all known cases, but not generally in even degrees.]