Characters of Kac-Moody algebra from orbifold

In a Wess–Zumino–Witten model on some Lie group G, the character of a particular integrable representation is the same as the specialized character from the corresponding Kac-Moody algebra. Suppose now we have a WZW model on an orbifold, i.e. on G/H where H is a subgroup of the center of G, then how should we compute the WZW characters for this orbifold theory? In particular, are there any relation between the original characters (WZW on G) and the orbifold characters (WZW on G/H)?

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In particular, how can one decomposite the representations of affine G into representations of affine G/H? This should be the first step of the question. – Moduli Oct 14 '10 at 15:51