  We calculate equivariant elliptic cohomology of the partial flag variety G/H,
where H \subseteq G are compact connected Lie groups of equal rank.
  We identify the RO(G)-graded coefficients Ell_G^* as powers of Looijenga's
line bundle and prove that transfer along the map {\pi}: G/H -\rightarrow pt is
calculated by the Weyl-Kac character formula.
  Treating ordinary cohomology, K-theory and elliptic cohomology in parallel,
this paper organizes the theoretical framework for the elliptic Schubert
calculus of [N.Ganter and A.Ram, Elliptic Schubert calculus. In preparation].
