Group communication provides primitives that ensure reliable and ordered delivery of messages to a group of destinations. It is an important building block for replicated fault-tolerant applications such as replicated databases. In the past, most group communication systems have been monolithic. Recent group communication systems have been built around components, allowing for more flexibility. In this paper, we propose a novel approach to the composition of group communication protocols. In this approach, components are modeled as finite state machines communicating via signals. We introduce two building blocks, called \emph{adaptor} and \emph{adaplexor}, that facilitate the development and the composition of group communication protocol stacks, and we discuss how isolation can be achieved in this setting. To validate our architectural concepts, we have implemented the proposed group communication architecture in SDL.