According to a good friend of mine who is a principal engineer at Nexteer, they do.
Nexteer produces their products in 20 manufacturing plants worldwide and has 14 local customer support centers and five regional engineering centers. While the corporation is owned by Pacific Century Motors, 51% of them is owned by AVIC Automobile Industry Holdings, Nexteer's world headquarters is in Auburn Hills, Michigan.
If you are trying to get away from any one country in automotive manufacturing good luck, all the automotive suppliers are global corporations owned by investment groups from all nations and change often.