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Do you need access to the bare HTTP request in ASP.NET Web API to access custom header etc.? Then add the HttpRequestMessage:

public class CalculatorController : ApiController
{
  public int Add(HttpRequestMessage requestMessage, int x, int y)
  {
    var accessToken = requestMessage.Headers.Authorization.Parameter;
    // use the HTTP header

    return x + y;
  }
}

The HttpRequestMessage is automatically bound to the controller action, so you can still execute the action like http://localhost/calculator/add?x=3&y=2

Simple and easy.