Topeka ? What do Republican political strategist Karl Rove, the Kansas Capitol renovation project and the Senate race in Virginia have in common?

Rove’s Crossroads GPS has unleashed new TV ads opposing Democratic candidates in several states.

One of those ads targets Tim Kaine, the Democratic Senate candidate in Virginia. The ad alleges that Kaine supported spending $39 million on “office upgrades for politicians.”

PolitiFact has looked at the allegation and said it was “mostly false.” The “office upgrades for politicians” allegation is based on Kaine’s support of President Barack Obama’s stimulus bill, part of which included a special bond program, called Build America Bonds, which was created to help state and local governments save money on capital projects. And Kaine had nothing to do with approval of the bonds in Kansas.

In Kansas, officials approved using the program to pay for $39 million of the Capitol renovation plan. The lower borrowing costs for the bonds would save Kansas about $840,000 in debt service costs, state officials said at the time it was approved in 2009.

Crossroads GPS has been criticized for ads in several states.