The homology mod 2 of the free loop group of a compact, connected, simply connected Lie group \(G\) is determined by the homology of \(G\) and of the (based) loop space of \(G\), the algebra structure depends on the homology of the adjoint map, \(ad\;:\;G\times\Omega G\rightarrow \Omega G\).
This technical paper determines \(H_\ast (ad,{\mathbb{Z}}/2{\mathbb{Z}})\) for the exceptional Lie groups \(G=G_2, F_4,E_6\) and \(E_7\). It relies partially on previous results by A. Kono and K. Kozima [Proc. R. Soc. Edinb., Sect. A 112, No. 3/4, 187-202 (1989; Zbl 0677.55008); J. Math. Soc. Japan 45, No. 3, 495-510 (1993 ; Zbl 0795.57015)]. Complementary information is also given on Steenrod algebra actions and Hopf algebra structures on the (based) loop spaces homology of exceptional Lie groups.