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Let $\theta$ be an automorphism of a thick irreducible spherical building$\Delta$ of rank at least $3$ with no Fano plane residues. We prove that ifthere exist both type $J_1$ and $J_2$ simplices of $\Delta$ mapped ontoopposite simplices by $\theta$, then there exists a type $J_1\cup J_2$ simplexof $\Delta$ mapped onto an opposite simplex by $\theta$. This property iscalled "cappedness". We give applications of cappedness to opposition diagrams,domesticity, and the calculation of displacement in spherical buildings. In acompanion piece to this paper we study the thick irreducible sphericalbuildings containing Fano plane residues. In these buildings automorphisms arenot necessarily capped.

Opposition diagrams for automorphisms of large spherical buildings