  In this paper we describe a systematic method to compute elliptic genera of
(2,2) supersymmetric gauge theories in two dimensions with gauge group G/Gamma
(for G semisimple and simply-connected, Gamma a subgroup of the center of G)
with various discrete theta angles. We apply the technique to examples of pure
gauge theories with low-rank gauge groups. Our results are consistent with
expectations from decomposition of two-dimensional theories with finite global
one-form symmetries and with computations of supersymmetry breaking for some
discrete theta angles in pure gauge theories. Finally, we make predictions for
the elliptic genera of all the other remaining pure gauge theories by applying
decomposition and matching to known supersymmetry breaking patterns.
