A CLASSIFICATION RESULT FOR APPROXIMATELY HOMOGENEOUS C-ASTERISK-ALGEBRAS OF REAL RANK ZERO

We prove that the total K-theory group (K) under bar(-) = +(infinity)( n=0) K(-;Z/n) equiped with a natural order structure and acted upon b y the Bockstein operations is a complete invariant for a class of appr oximately subhomogeneous C-algebras of real rank zero which include t he inductive limits of systems of the form P1Mn(1)(C(X-1))P-1-->P2Mn(2 )(C(X-2))P-2-->... where Pi are selfadjoint projections in M-n(i)(C(X- i)) and X-i are finite (possibly disconnected) CW complexes whose dime nsions satisfy a certain growth condition. The problem of finding suit able invariants for the study of C-algebras of this type was proposed by Effros. Our result represents a substantial generalization of the classification theorem of approximately finite dimensional (AF) C-alg ebras, due to Elliott.