  We generalize the notion of Ekedahl-Oort strata to elements in the loop group
of any connected reductive group, and call the resulting discrete invariant the
truncation of level 1 of the element. We give conditions for the Newton points
occurring among the elements of a given truncation of level 1 and especially
for the generic Newton point in a given truncation stratum. We prove that
truncation strata are locally closed and give a description of the closure of
each stratum. We also translate our results back to the original Ekedahl-Oort
stratification of the reduction modulo p of Shimura varieties.

Algebraic Geometry