\begin{center} {\bf Endotrivial irreducible lattices}\\ \emph{Geoffrey R. Robinson,\\ Institute of Mathematics, University of Aberdeen,\\September 2010} \end{center} \begin{abstract} We consider the structure of a finite group which has a faithful irreducible endotrivial $RG$-module for a suitable complete discrete valuation ring $R$ with $R/J(R)$ of characteristic $p.$ \end{abstract}