Question: Detroit, MI is the center of Class B airspace, however a good portion of that airspace within the inverted wedding cake is in Canada. What are the mechanisms that allow US to define Class B airspace force and effect in Canada?

The VFR Terminal chart for reference:
<https://aeronav.faa.gov/content/aeronav/tac_files/PDFs/Detroit_TAC_91_P.pdf>

Answer: 
The portion over Canada is not designated US Class B but Canadian Class C. 

Note that Canadian Class C airspace definition is similar to US Class B. In particular, VFR aircraft must obtain clearance prior to entry. A mode C transponder is required.

To add: airspace over Canada is generally managed by [NAV CANADA](https://en.wikipedia.org/wiki/Nav_Canada). Definition for the Canadian side of the Detroit Terminal Control Area (TCA) can be found in NAV CANADA's [Designated Airspace Handbook](https://www.navcanada.ca/EN/products-and-services/Documents/DAH_Current_EN.pdf), portions excerpted below (from page 78):

[![Summary for Detroit TCA bounding coordinates](https://i.stack.imgur.com/174ME.png)](https://i.stack.imgur.com/174ME.png)

We can see that these definitions matches the eastern portions of the Detroit TCA exactly, e.g, the outer area altitudes from 6,000' to 10,000' bounded 30nm from the Detroit VOR (DXO).

The Detroit TCA airspace was modified a few years ago, which required coordination between the FAA and Nav Canada. The following discussion from the [US Federal Register](https://www.govinfo.gov/content/pkg/FR-2014-01-21/pdf/2014-00622.pdf) (page 3307) may be of further interest:

> 
> Also, as noted in the NPRM, the
>  eastern portion of the DTW Class B
>  airspace area extends into Canadian
>  airspace. The equivalent Canadian
>  airspace to Class B airspace, as
>  designated in the United States, is Class
>  C airspace. NAV CANADA, the
>  Canadian air service navigation
>  provider, generally designates Class C
>  airspace with a 12,500 feet MSL ceiling,
>  however, has advised the FAA of its
>  willingness to establish corresponding
>  Canadian Class C airspace adjoining the
>  FAA’s DTW Class B airspace with a
>  ceiling of 10,000 feet MSL.
>  Additionally, NAV CANADA advised it
>  would make the Canadian Class C
>  airspace action effective to match the
>  effective date of this DTW Class B
>  airspace modification action. 
> 
> 
>
All airspace in each FIR (or UIR) is by default controlled by the corresponding ACC (US: ARTCC). In the case of metro Detroit, it's Cleveland FIR/ARTCC on the US side and Toronto FIR/ACC on the Canadian side.

All other controlling agencies get their airspace by delegation from the ACC via an LOA. Cleveland ARTCC delegates the airspace on the US side to Detroit TRACON, and Toronto FIR/ACC delegates the airspace on the Canadian side *also* to Detroit TRACON. So, despite being a US agency, Detroit TRACON ends up controlling airspace in Canada as well. This is common along international borders, even in places where the land border isn't as well agreed as the US/Canada one.