  Fiber bundles over infinite fields with non-trivial ultra-norms are
considered. For them geometric wrap groups are defined and investigated.
Besides fields also Cayley-Dickson algebras over fields of characteristic not
equal to two are taken into account. For fibers over them wrap groups are
introduced and their structure is investigated. Different classes of smoothness
for wrap groups are used. It is demonstrated that generally such groups are
infinite dimensional over the corresponding field and totally disconnected
groups. That is, they are continuous or differentiable non-archimedean
differentiable uniform spaces and the composition $(f,g)\mapsto f^{-1}g$ is
continuous or differentiable depending on a class of smoothness of groups. Skew
products of wrap groups are studied as well.
