Title: The mod 2 cohomology of the infinite families of Coxeter groups of type B and D as almost Hopf rings,
Abstract: We describe a Hopf ring structure on the direct sum of the cohomology groups
$\bigoplus_{n \geq 0} H^* \left( B_n; \mathbb{Z}_2 \right)$ of the Coxeter
groups of type $B_n$, and an almost-Hopf ring structure on the direct sum of
the cohomology groups $\bigoplus_{n \geq 0} H^* \left( D_n; \mathbb{Z}_2
\right)$ of the Coxeter groups of type $D_n$, with coefficient in the field
with two elements $\mathbb{Z}_2$. We give presentations with generators and
relations, determine additive bases and compute the Steenrod algebra action.
The generators are described both in terms of a geometric construction by De
Concini and Salvetti and in terms of their restriction to elementary abelian
2-subgroups.