  We extend the group theoretic construction of local models of Pappas and Zhu
to the case of groups obtained by Weil restriction along a possibly wildly
ramified extension. This completes the construction of local models for all
reductive groups when $p \geq 5$. We show that the local models are normal with
special fiber reduced and study the monodromy action on the sheaves of nearby
cycles. As a consequence, we prove a conjecture of Kottwitz that the
semi-simple trace of Frobenius gives a central function in the parahoric Hecke
algebra. We also introduce a notion of splitting model and use this to study
the inertial action in the case of an unramified group.
