I'm sure there's an international protocol and convention to deal with issues such as these.
As far as I am aware, the lead investigator would be the state where the accident took place, assuming that state declares it to be an accident, as opposed to an incident. (I believe any incident involving serious or fatal injuries is classed as an accident; a very serious incident - for example the Interflug A310 which went into aerobatics near Moscow in 1991 - would not necessarily be the subject of a formal accident report).
In a situation such as this, the state of registry and the state of manufacture would also be involved, to the extent that they are invited to do so; the formal report would be compiled by the state where the accident took place and (as evidenced by the SQ TPE or KLM Tenerife disasters), they might not always agree.
I would imagine that the investigating authority would also have the right to call another body/consultants in to assist; for example, if there was repeat of (for example) SR 111, the Canadian TSB would most likely be invited to assist, having built up considerable experience in a particular area.