rewrite - Nginx convert subdomain to path component without redirect

Question

The idea is to take incoming requests to http://abc.example.com/... and rewrite them to http://example.com/abc/...

That's easy enough to do with a 301/302 redirect:

# rewrite via 301 Moved Permanently
server {
  listen 80;
  server_name abc.example.com;
  rewrite ^ $scheme://example.com/abc$request_uri permanent;
}

The trick is to do this URL change transparently to the client when abc.example.com and example.com point at the same Nginx instance.

Put differently, can Nginx serve the contents from example.com/abc/... when abc.example.com/... is requested and without another client round trip?

Starting Point Config

Nginx config that accomplishes the task with a 301:

# abc.example.com
server {
  listen 80;
  server_name abc.example.com;
  rewrite ^ $scheme://example.com/abc$request_uri permanent;
}

# example.com
server {
  listen 80;
  server_name example.com;
  location / { 
    # ...
  }
}

Answer 1

# abc.example.com
server {
  listen 80;
  server_name abc.example.com;
  location / {
    proxy_pass http://127.0.0.1/abc$request_uri;
    proxy_set_header Host example.com;
  }
}