Sums of values of non-principal characters over shifted primes

For a nonprincipal character $\chi$ modulo $D$, when $x\ge D^{\frac{5}{6}+\epsilon }$, $(l,D)=1$, we prove a nontrivial estimate of the form ${\sum }_{n\le x}\mathrm{\Lambda }(n)\chi (n-l)\ll x\exp (-0.6\sqrt{\ln D})$ for the sum of values of $\chi$ over a sequence of shifted primes. Bibliography: 41 references.