The Kenya birth certificate is purported to be the actual BC by detractors of Obama as a US citizen.
Main point is that if Obama was not born in the US in the year generally accepted as his birth year, 1962, then Obama is not a citizen at all, according to US citizenship law in effect at that time.
If his mother was actually Stanley Dunham, she was too young at 18 to transfer citizenship to a baby born outside the US. She needed to be a permanent resident in the US for at least 5 years after her 14th birthday.
Biggest issue surrounding the Hawaiian BC is that it was just a necessary mechanism to prove he was born in the US. Without that BC he's not a citizen at birth at all.
The presence/proof of an authentic birth certificate showing birth outside the US means the Hawaiian BC was not legitimate. It's a kill shot.
Soetero, allegedly, came later and adopted Obama. I don't know if adoption changes the child's name all the way back to a BC, which would be the only reason, as I see it, for Soetero to have anything to do with a BC.
Soetero adopting Obama would have nothing to do with US citizenship. If Obama was a US citizen it can't be taken away when he was a minor child. If Indonesia has a no dual citizenship rule, that applies to Indonesians who want to change. They have to give up their Indonesian citizenship to take another. Indonesia has no authority to take away another country's citizenship. US doesn't have any dual citizenship rules.