As an investment vehicle for the IRA, you can open an LLC either in the US or offshore. A self-directed IRA in an offshore LLC is also sometimes called an Offshore IRA.
An offshore LLC offers the advantage of asset protection. However, it comes with increased costs as it requires both local and US filings.
A self-directed IRA without an LLC does not leverage the full benefits. Without being placed into an LLC, the IRA is controlled by a custodian, and you direct the custodian. However, you do not control the assets yourself and must rely on the custodian to carry out your wishes. The US investment advisor is bound by US regulations.
Only if you place the IRA into an offshore LLC will you as LLC manager have full control. The only US regulation you have to comply with is tax reporting. You would have to file a form 5471 for the offshore LLC or potentially make a check-the-box election to minimize this reporting requirement.