He tried to do so many things to purge voting rolls, it's hard to find a place to start. The biggest thing was when he was AG and helped get some laws passed that made it more difficult for some to vote. The law had two basic parts: need photo ID to vote and new KS voters needed to provide proof of citizenship. His claim was that illegal immigrants were voting and others were voting on behalf of dead people. He said something to the effect that 36,000 illegals were voting and 2000 others were voting on behalf of the dead. The problem with Kobach is that he makes these claims with no proof that it is a problem. While AG his office found less than 10 cases of actual voter fraud. If I remember right, most were older people who somehow got confused (moved from another state and double voted). Voter ID laws wouldn't have stopped this btw
While voter fraud certainly does exist, it does not exist in the numbers that KK claims. In a three year period, he excluded 36,000 residents from the voting rolls because they didn't meet the qualifications. Eventually the courts said it was unconsitutional to have to prove citizenship because the judge stated (correctly) you cannot take away voting rights for thousands of legal voters to stop a mythical problem. He was ordered to put about 18,000 people back on the voter rolls. It took him 18 months to do this. For this, he was found in contempt.
Basically he created a system that was so confusing that local voting officials weren't even sure what to do. This is just one example. Look into him. There is plenty more out there