Large character sums with multiplicative coefficients

In this paper, we investigate large values of Dirichlet character sums with multiplicative coefficients ${\sum }_{n\le N}f(n)\chi (n)$. We prove a new Omega result in the region $\exp ((\log q{)}^{\frac{1}{2}+\delta })\le N\le \sqrt{q}$, where $q$ is the prime modulus.