Given a height at most two Landweber exact $\mathbb {E}_\infty$-ring $E$ whose homotopy is concentrated in even degrees, we show that any complex orientation of $E$ which satisfies the Ando criterion admits a unique lift to an $\mathbb {E}_\infty$-complex orientation $\mathrm {MU} \to E$. As a consequence, we give a short proof that the level $n$ elliptic genus lifts uniquely to an $\mathbb {E}_\infty$-complex orientation $\mathrm {MU} \to \mathrm {tmf}_1 (n)$ for all $n\, {\geq}\, 2$.

Motivated by complex oriented equivariant cohomology theories, we give a natural algebraic definition of an $A$-equivariant formal group law for any abelian compact Lie group $A$. The complex orientedcohomology of the classifying space for line bundles gives an example.We also show how the choice of a complete flag gives rise to a basis and a means of calculation. This allows us to deduce thatthere is a universal ring $L_A$ for $A$-equivariant formal group laws and that it is generated by the Euler classes and the coefficients of the coproduct of the orientation. Westudy a number of topological cases in some detail. 1991 Mathematics Subject Classification: 14L05, 55N22, 55N91, 57R85.