Archey, Dawn Elizabeth, 1979-2008-12-202008-12-202008-06https://hdl.handle.net/1794/8155viii, 107 p. A print copy of this thesis is available through the UO Libraries. Search the library catalog for the location and call number.This dissertation consists of two related parts. In the first portion we use the tracial Rokhlin property for actions of a finite group G on stably finite simple unital C *-algebras containing enough projections. The main results of this part of the dissertation are as follows. Let A be a stably finite simple unital C *-algebra and suppose a is an action of a finite group G with the tracial Rokhlin property. Suppose A has real rank zero, stable rank one, and suppose the order on projections over A is determined by traces. Then the crossed product algebra C * ( G, A, à à ±) also has these three properties. In the second portion of the dissertation we introduce an analogue of the tracial Rokhlin property for C *-algebras which may not have any nontrivial projections called the projection free tracial Rokhlin property . Using this we show that under certain conditions if A is an infinite dimensional simple unital C *-algebra with stable rank one and à à ± is an action of a finite group G with the projection free tracial Rokhlin property, then C * ( G, A, à à ±) also has stable rank one.en-USMathematicsCuntz subequivalenceStable rank oneTracial Rokhlin propertyFinite group actionsCrossed productC*-algebrasThesis