  We propose a formalism to capture the structure of the equivariant bordism
rings of smooth manifolds with commuting involutions. We introduce the concept
of an oriented el$_2^{RO}$-algebra, an algebraic structure featuring
representation graded rings for all elementary abelian 2-groups, connected by
restriction homomorphisms, a pre-Euler class, and an inverse Thom class; this
data is subject to one exactness property. Besides equivariant bordism,
oriented global ring spectra also give rise to oriented el$_2^{RO}$-algebras,
so examples abound. Inverting the inverse Thom classes yields a global
2-torsion group law. In this sense, our oriented el$_2^{RO}$-algebras are
delocalized generalizations of global 2-torsion group laws.
  Our main result shows that equivariant bordism for elementary abelian
2-groups is an initial oriented el$_2^{RO}$-algebra. Several other interesting
equivariant homology theories can also be characterized, on elementary abelian
2-groups, by similar universal properties. We prove that stable equivariant
bordism is an initial el$_2^{RO}$-algebra with an invertible orientation; that
Bredon homology with constant mod 2 coefficients is an initial
el$_2^{RO}$-algebra with an additive orientation; and that Borel equivariant
homology with mod 2 coefficients is an initial el$_2^{RO}$-algebra with an
orientation that is both additive and invertible.
