diff --git a/async_lru/__init__.py b/async_lru/__init__.py
index ecca5fdd..6da57efb 100644
--- a/async_lru/__init__.py
+++ b/async_lru/__init__.py
@@ -4,6 +4,7 @@
 from asyncio.coroutines import _is_coroutine  # type: ignore[attr-defined]
 from functools import _CacheInfo, _make_key, partial, partialmethod
 from typing import (
+    Any,
     Callable,
     Coroutine,
     Generic,
@@ -208,8 +209,7 @@ async def __call__(self, /, *fn_args: _P.args, **fn_kwargs: _P.kwargs) -> _R:
             return cache_item.fut.result()
 
         fut = loop.create_future()
-        coro = self.__wrapped__(*fn_args, **fn_kwargs)
-        task = loop.create_task(coro)
+        task = loop.create_task(self.__wrapped__(*fn_args, **fn_kwargs))
         self.__tasks.add(task)
         task.add_done_callback(partial(self._task_done_callback, fut, key))
 
@@ -280,7 +280,7 @@ def __init__(
         self.__wrapper = wrapper
 
     def cache_invalidate(self, /, *args: _P.args, **kwargs: _P.kwargs) -> bool:
-        return self.__wrapper.cache_invalidate(self.__instance, *args, **kwargs)
+        return self.__wrapper.cache_invalidate(self.__instance, *args, **kwargs)  # type: ignore[arg-type]
 
     def cache_clear(self) -> None:
         self.__wrapper.cache_clear()
@@ -296,8 +296,8 @@ def cache_info(self) -> _CacheInfo:
     def cache_parameters(self) -> _CacheParameters:
         return self.__wrapper.cache_parameters()
 
-    async def __call__(self, /, *fn_args: _P.args, **fn_kwargs: _P.kwargs) -> _R:
-        return await self.__wrapper(self.__instance, *fn_args, **fn_kwargs)  # type: ignore[arg-type]
+    async def __call__(self, /, *args: _P.args, **kwargs: _P.kwargs) -> _R:
+        return self.__wrapper.cache_invalidate(self.__instance, *args, **kwargs)  # type: ignore[arg-type]
 
 
 def _make_wrapper(
@@ -320,7 +320,10 @@ def wrapper(
         if hasattr(fn, "_make_unbound_method"):
             fn = fn._make_unbound_method()
 
-        return _LRUCacheWrapper(fn, maxsize, typed, ttl)
+        wrapper = _LRUCacheWrapper(fn, maxsize, typed, ttl)
+        if sys.version_info >= (3, 12):
+            wrapper = inspect.markcoroutinefunction(wrapper)
+        return wrapper
 
     return wrapper