Ummah is often translated as the Muslim community and then treated as though it named an entity that could act, decide or be represented. It cannot, and reading it that way misses what the word is for.
There is no register of the ummah. There is no council, no officer, no procedure by which it reaches a decision, and no body that speaks for it. Anyone described in the press as a leader of the world's Muslims is not one, and no such position exists.
What the word asserts is that the bond of faith constitutes a real community, and that this community takes precedence over the bonds that ordinarily organise people: descent, tribe, language, nation and citizenship. In the Arabian context in which it was first used, displacing tribal loyalty was a radical and dangerous claim rather than a piety, and it remains a theological statement before it is a description of anything.
The claim has practical consequences that are easy to observe. Prayer everywhere is oriented to one point. Pilgrimage converges annually on that point from every country. Alms flow across borders on the assumption that a Muslim in need has a claim on a Muslim with means, wherever either of them lives. And the suffering of Muslims in one country is treated, without further argument, as the business of Muslims in another, which shapes contemporary politics in ways that are unintelligible if the concept is read as a demographic label.
The historical usage is wider than the modern one. The word appears in the Qur'an in several senses, and the document known as the Constitution of Medina applies it to a community that included the Jewish tribes of the city, which is a political rather than a confessional usage.
Efforts to convert the theological claim into an institution have all failed. The late Ottoman revival of the caliphate as a pan-Islamic focus, the abolition of that caliphate in 1924, and the founding of the Organisation of Islamic Cooperation as an association of states have each been read by someone as the ummah taking form, and none has been generally accepted as speaking for it.