Foreign fund management companies may not establish branches in Switzerland.
"Art. 52 Duty to obtain authorisation
1 Authorisation from FINMA is required by financial institutions that have their registered office abroad (foreign financial institutions) and that wish to establish a branch in Switzerland that employs persons who perform any of the following activities in the name of the foreign financial institution on a permanent commercial basis in Switzerland or from Switzerland: [...]
2 Foreign fund management companies may not establish branches in Switzerland. [...]" (Federal Act on Financial Institutions (RO 2018 5247, 15 June 2018), last amended on 18 February 2020, Article 52 [unofficial translation])
Federal Act on Financial Institutions (RO 2018 5247, 15 June 2018), last amended on 18 February 2020, Article 52
[<a href="https://www.fedlex.admin.ch/eli/cc/2018/801/en">Act</a>]