The role of the extended Lorentz group as an invariance of physical theories is re-examined. Contrary to common acceptance it is asserted that all known theories, including those that describe the weak interactions exhibit invariance under the extended Lorentz group of frame transformations. The fundamental discrete transformations are defined, independent of any particular field system, as endomorphisms on the space of spin frames over space-time. The appropriate transformations for spinor fields are considered in detail, and the notions of covariance under frame reversal is contrasted with other notions of 'parity invariance'.