  We develop the concept of weak tracial Rokhlin property for finite group
actions on simple (not necessarily unital) C*-algebras and study its properties
systematically. In particular, we show that this property is stable under
restriction to invariant hereditary C*-algebras, minimal tensor products, and
direct limits of actions. Some of these results are new even in the unital case
and answer open questions asked by N. C. Phillips in full generality. We
present several examples of finite group actions with the weak tracial Rokhlin
property on simple stably projectionless C*-algebras. We prove that if $\alpha
\colon G \rightarrow \mathrm{Aut}(A)$ is an action of a finite group $G$ on a
simple C*-algebra $A$ with tracial rank zero and $\alpha$ has the weak tracial
Rokhlin property, then the crossed product $A \rtimes _{\alpha} G$ and the
fixed point algebra $A^{\alpha}$ are simple with tracial rank zero. This
extends a result of N. C. Phillips to the nonunital case. We use the machinery
of Cuntz subequivalence to work in this nonunital setting.
