No, Oyster does not facilitate the actual grant of equity to Team Members - that is, the grant letter must be between you and your team member. However, we can help you navigate awarding equity compliantly to your team members across the globe.
Because your team member is technically employed by Oyster and not by your company, it is important that your equity plan allows for equity awards to non-employees. Most company equity schemes allow you to provide share options to non-employees (typically called "non-qualified stock options (NSOs)" or "unapproved options").
These share schemes are typically not as tax advantageous for the employee as your home entity country share schemes - we recommend speaking to your equity provider to understand the details for both your company and your employees.