There seems to be some confusion of terminology here. In Direct3D, you have threads and thread groups. "work item" and "work group" are generally encountered in OpenCL terminology, where a "work item" would be what a thread is in Direct3D and a "work group" corresponds to a Direct3D thread group.
groupshared memory is memory accessible to all threads that are part of the same thread group.
It is unclear what exactly you mean by "manipulating L1 cache directly". A cache is a hardware component that is used to transparently optimize memory access. The word "transparent" is crucial here. While, at the hardware level, caches necessarily contain some form of memory, they are generally not explicitly "accessible" as a region of storage. You can't have a pointer that points into a cache. You can have a pointer that points into memory. Memory accesses will typically go through a cache, i.e., any memory request will be handed off to the next cache, which can then check whether it can serve the request directly or has to go further down the memory hierarchy. There's more to a cache than just the memory it uses to cache stuff. A cache also contains additional logic for managing the cache on top of just the storage itself. Caches are implicit by nature. As you manipulate memory, you will typically also cause some caches to manipulate their memory along the way. But you generally can't "manipulate" a cache directly in the sense of explicitly defining what is when to be stored where in the cache. As soon as you can explicitly point into it and read/write from/to it, it kinda stops being a cache and starts being just some form of storage.
That being said,
groupshared memory is generally located in fast on-chip storage just like caches are. The whole point of
groupshared memory is to take advantage of the knowledge that certain threads reside on the same part of the chip to allow them to communicate faster. And on some hardware (e.g., most of the recent NVIDIA architectures),
groupshared memory and the L1 cache will actually use the same physical memory. However, that just means that one part of that memory is used as "normal" memory, accessed directly via addressing through some load-store-unit, while another part is used by the L1 cache to cache stuff…