I wonder under what US non immigrant visa category a foreigner can come into the US and open a business and work as an owner/manager? http://travel.state.gov/content/visas/en/general/all-visa-ca...

For example the requirement for B-1 (business visa) makes it clear that you are supposed to stay temporarily and not here to work:

"For example, additional requested documents may include evidence of:

The purpose of your trip; Your intent to depart the United States after your trip; and/or Your ability to pay all costs of the trip. Evidence of your employment and/or your family ties may be sufficient to show the purpose of your trip and your intent to return to your home country. " http://travel.state.gov/content/visas/en/visit/visitor.html