Strange modular expression in paper on group signatures
In this context $1/e_i$ (more commonly written as $e_i^{-1}$) stands for the multiplicative inverse of $e_i$ modulo the relevant modulus, which in this case is $\lambda(n) = \text{lcm}(p-1,q-1)$.  That is, $1/e_i$ is that value $f$ such that $f \cdot e_i = k \cdot \text{lcm}(p-1, q-1) + 1$, for some integer $k$.

Given the factorization of $n$, we can compute $1/e_i$ using the Extended Euclidean method.

We also believe that that $(C_2 \cdot a_0)^{1/e_i} \bmod n$ cannot be computed without knowing the factorization $n = p \cdot q$ (for general $C_2, a_0, e_i$); in fact, this is precisely the RSA problem.