Equivariant K Theory and Freeness of Group Actions on C* Algebras Freeness of an action of a compact Lie group on a compact Hausdorff space is equivalent to a simple condition on the corresponding equivariant K theory. This fact can be regarded as a theorem on actions on a commutative C* algebra namely the algebra of continuous complex valued functions on the space. The successes of noncommutative topology suggest that one should try to generalize this result to actions on arbitrary C* algebras. Lacking an appropriate definition of a free action on a C* algebra one is led instead to the study of actions satisfying conditions on equivariant K theory in the cases of spaces simply freeness. The first third of this book is a detailed exposition of equivariant K theory and KK theory assuming only a general knowledge of C* algebras and some ordinary K theory. It continues with the authors research on K theoretic freeness of actions. It is shown that many properties of freeness generalize while others do not and that certain forms of K theoretic freeness are related to other noncommutative measures of freeness such as the Connes spectrum. The implications of K theoretic freeness for actions on type I and AF algebras are also examined and in these cases K theoretic freeness is characterized analytically