Étale wild kernels of exceptional number fields

We clarify the relationship between higher étale wild kernels of a number field at the prime 2 and the Galois-coinvariants of Tate-twisted class groups in the 2-cyclotomic tower of the field. We also determine the relationship between the étale wild kernel and the group of infinitely divisible elements of H2(F,Z2(j+1)){2}.