By N. Christopher Phillips

Freeness of an motion of a compact Lie workforce on a compact Hausdorff house is reminiscent of an easy at the corresponding equivariant K-theory. This truth should be considered as a theorem on activities on a commutative C*-algebra, particularly the algebra of constant complex-valued features at the area. The successes of "noncommutative topology" recommend that one should still attempt to generalize this outcome to activities on arbitrary C*-algebras. missing a suitable definition of a loose motion on a C*-algebra, one is led as an alternative to the learn of activities gratifying stipulations on equivariant K-theory - within the instances of areas, easily freeness. the 1st 3rd of this ebook is a close exposition of equivariant K-theory and KK-theory, assuming just a common wisdom of C*-algebras and a few usual K-theory. It maintains with the author's study on K-theoretic freeness of activities. it's proven that many houses of freeness generalize, whereas others don't, and that yes kinds of K-theoretic freeness are relating to different noncommutative measures of freeness, similar to the Connes spectrum. the results of K-theoretic freeness for activities on sort I and AF algebras also are tested, and in those circumstances K-theoretic freeness is characterised analytically.